This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
z)}Considering a set of functions only dependent of the beam axis coordinate {u(x); v(x); w(x)} as the corresponding amplitudes of the previous cross section interpolations, the beam displacement field is described as u(x,y,z) = u(x) (p(y,z); v(x,y,z) = v(x) Y(y,z); w(x,y,z) = w(x) x(y,z). Admitting the cross section to be constituted by a set of elements, assembled in such a way that the compatibility between them is satisfied, the set of the differential equilibrium equations can then be written in a compact form: [K 1 ]8 ff +[K 2 ]6'+[K 3 ]8=0 where: 8 = {u(x), v(x), w(x)}; Ki and K3 are symmetric and K2 skew-symmetric. The solution procedure for the equilibrium equations is related to that of a generalized eigenvalue problem, which permits to obtain a set of orthogonal deformation modes. The generalized eigenvalue problem is achieved by an assumption of the solution form, suggested by the theorem of Toupin concerning the quantification of Saint-Venant Principle. A procedure based on a quadratic eigenvalue problem is also considered for the solution of the differential equations, which is verified to lead to identical results. The governing differential equilibrium equations are solved numerically by the conventional finite element method over the beam axis, adopting Hermite functions for the amplitudes {u(x), v(x), w(x)}. Numerical examples are presented for the analysis of a thin walled beam. Some important conclusions can be drawn from the analysis of results, namely: i) the set of deformation modes of most relevance for a specific cross section subjected to a specific load can be clearly identified; ii) the solution decay behaviour of higher order modes is observed and iii) the solutions obtained from the generalized eigenvalue problem are in excellent agreement with those obtained trough the quadratic eigenvalue procedure.
— 228 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Research on Simulation Analysis for Stability Problem of PressurePenstock with Imperfection Wenyuan Meng **, Xiuqin Li \ Jiashou Zhuo 2 1
North China Institute of Water Conservancy and Hydroelectric Power, Personnel Department, Zhengzhou, Henan, 450008 China 2 College of Civil Engineering, Hohai University, Nanjing, Jiangsu, 210098 China Email: [email protected] Abstract The construction of large-scale hydropower stations and large-capacity pumped-storage power stations make penstocks construction be large-scale and huge-scale. The use of high quality steel makes penstocks become more and more flexible and thin. The stability of penstock has become the key factor in penstock design. In this paper the simulating technology of Element-Free Method and experiment is applied to the research on the stability analysis of penstock under external pressure. After a brief review of the element-free method (EFM) and the stability analysis of pressure penstock, a numerical model is established for the stability analysis of geometric nonlinear ribbed shell with initial imperfections. At the same time, the seams between penstock and concrete were turned into initial imperfections. Some improvement on the EFM is presented, including a method for constructing the field function of EFM. The thick curved-beam geometry equation and the nonlinearity geometry equation of thin shell with initial geometric imperfections are derived. This geometry equation can be conveniently reduced to the cases of perfect shell and linear shell. The model of ribbed shell is regarded as the combination of thick curved-beam and thin shell. This model can reflect the real stress and strain state of penstock. Finally, as one of the key works in this paper, the experimental scheme for the stability analysis of penstock under negative-pressure is presented. With the help of experiments, the buckling mechanism of perfect penstock and imperfect penstock are investigated. The reliability of new model is verified. The sensitivity of critical load to imperfection and geometric size is analyzed.
— 213 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Research on Thermo Quality Transmission Problems for Large-Scale Slab with Creep* J. X.Wang 1 ' 2 *, X.C.Wang 2 1
Key Lab for the Prevention and Control of Explosion Disaster, Beijing Institute of Technology, Beijing, 100081 China 2 College of Architecture and Civil Engineering, North China University of Technology, Beijing, 100041 China Email: [email protected] Abstract Based on Biot theory, the basic equations for large-scale slab are presented and the transient thermal or thermo-mechanical loading are considered, four types of material surface of large-scale slab forced by transient thermal or thermo-mechanical loading are discussed. The characteristics and regularity of heat quality transmission in large-scale slab were investigated. The displacement fields and pore pressure is obtained by using the formulation of the corresponding transient thermal loading. There is significance for the research on thermo quality transmission problems of large-scale slab with permeates flow and creep. Biot's work was nonlinear and 3-demensional, it marked that the general idea of fluid permeates in large-scale slab had been set up. A series of achievement has been given about the question for study or discussion of fluid permeation, for instance, in geomechanics and biomechanics and so on. But the results for the thermal quality transmission of large-scale slab with permeate flow and creep are less presented in the literature. Wang has investigated its theory and application considering thermal elasticity and thermal loading, some important conclusion has been presented. Based on this method, the displacement fields and pore pressure are obtained in this paper. REFERENCES 1. Wang JX, Wang XC. Constitutive relation of thermo-elasto-plastic impact problems for frozen soil porous medium, in: Mechanical properties of advanced engineering materials, Tsinghua University Press & Springer-Verlag, 2003, pp. 69-75. 2. Wang JX, Wang XC. Numerical analysis of contact thermo-elastic-plasticity problems with creep for frozen soil, in: Mechanical properties of advanced engineering materials, Tsinghua University Press & Springer-Verlag, 2003, pp. 63-68.
* The investigation was supported by the grant of the Knowledge Innovation Program of the Chinese Academy of Sciences (No.: KZCX1-SW-04); Scientific Research Common Program of Beijing Municipal Commission of Education (No.:KM200610009010), Beijing Natural Science Foundation Program and Scientific Research Key Program of Beijing Municipal Commission of Education (No. :KZ200610009005). — 246 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Second-Order Analysis for Steel Frame Structures with a Distributed Plasticity Numerical Model Ke Wang1*, L. W. Tong \ Tian Li 2 College of Civil Engineering, Tongji University, Shanghai, 200092 China School of Civil Engineering, Zhengzhou University, Henan Zhengzhou, 450000 China Email: [email protected] Abstract This paper provides an efficient numeric model of steel frames using second-order distributed plasticity FEM (finite element method). Details of the modeling including element type, mesh discretization, material model, residual stresses, initial geometric imperfections, and boundary conditions are presented. Its validity is verified by several numerical examples. Case studies of Vogel's portal frame and space steel frames are performed. The ultimate loads obtained from the proposed analysis and Vogel agree well within 2% error. Therefore , the model is accurate and provides benchmark solutions of steel frames using second-order distributed plasticity analysis. The benchmark solutions of the steel frames are useful for the verification of various simplified second-order inelastic analyses. It is observed that the load carrying capacities calculated by the Code for design of Steel Structures (GB50017-2003) method are 20%~30% conservative when compared with those of the proposed analysis.and using this model the study was carried out on the effects of the nonlinear factors on the behavior of steel frames.
b
1
f
\f
HEA340
w
_JiF0= 1/400 CO UJ
cc UL X
I
7T*rr "^
mw ^
Horizontal displacement (mm)
Figure: Dimension and loading condition, and Comparison of horizontal load-displacement curves of Vogel's portal frame
REFERENCES 1. King WS, Chen WF. Practical second-order inelastic analysis of semirigid frames. Journal of Structural Engineering (ASCE), 1994; 120 (7): 2156-2175. 2. Seung-Eock Kim, Dong-Ho Lee. Second-order distributed plasticity analysis of space steel frames. Engineering Structures, 2002; 24: 735-744. — 225 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X,Aug. 21-23, 2006, Sanya, Hainan,China ©2006 Tsinghua University Press & Springer
Semi-Analytical Analysis of Super Tall Building Bundled-Tube Structures Yaoqing Gong *, Ke Li Civil Engineering School, Henan Polytechnic University, Jiaozuo, Henan, 454000 China Email: [email protected] Abstract A new semi-analytical method is developed for the analysis of interactions between the subgrade and the foundation and the superstructure of the super tall building bundled-tube structure by three-dimensional model which is a combination of stiffened-thin-wall tubes on semi-infinite elastic body. The subgrade is idealized as a semi-infinite elastic body, and the rigidities of the elastic body pertinent to various deformations of the foundation have been expressed as analytical equations [1], with which the reactions between the foundation and subgrade can be quantified expediently. The foundation is taken as a part of the superstructure. In fact, the foundation is the extension of the superstructure toward the underground. The only difference is the size, since in most cases the foundation must be large enough to make the soil stable. The superstructure and its foundation of the super tall building bundled-tube structure are simplified equivalently and continuously to a combination of stiffened-thin-wall tubes on semi-infinite elastic subgrade. Then discretization is made by some nodal lines, the unknown functions defined on the lines are used as primary unknowns, and interpolating functions are implemented between the lines. So the displacement field of the computing model can be expressed by the unknown functions. After using the principle of minimum potential energy, the governing equations will then be obtained, which is actually a group of ordinary differential equations. Therefore, analysis of a tall building structure will be changed into the solution of the boundary problem of a group of ordinary differential equations that can be solved by the precise and powerful Ordinary Differential Equation Solver — COLSYS [2], a kind of computational software. The interactions between the subgrade and the foundation and the superstructure of a super tall building bundled-tube structure due to static loadings are analyzed by the method based on the model. The numerical results show that the analytical model is reasonable and feasible. Therefore, a practicable method for the global analysis of the super tall building bundled-tube structure is obtained, and some valuable conclusions are acquired through analyzing the computing results as well. REFERENCES 1. Gong Yaoqing. Tall building structures on elastic subgrade and research of semi-analytical method. Tsinghua University Press, Beijing, China, 1999 (in Chinese). 2. Yuan Si. Introduction of a common compute program for boundary problems of ordinary differential equation—COLSYS. Computational Mechanics and Application, 1990; 2: 104-105, (in Chinese).
— 216 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X,Aug. 21-23, 2006, Sanya, Hainan,China ©2006 Tsinghua University Press & Springer
Simulation of Corrosion Rate of Carbon Steel Subjected to Elastic/ Plastic Strain M.Ridha 1 *, S.Aoki 2 1
Department of Mechanical Engineering,Syiah Kuala University, Banda Aceh, NAD, Indonesia Department of Computational Science and Engineering, Toyo University, Kawagoe, Saitama, Japan Email: [email protected]
2
Abstract In this research, the effects of elastric and plastic strain to the corrosion rate of carbon steel were studied. The corrosion rate of the steel was represented by its polarization curve. Experimental works using carbon steel plate specimen were carried out. The carbon steel plate was bended into U shape to initiate the elastic or plastic strain on the specimen. The U-bend type specimen was immersed into the artificial seawater and the polarization curves were measured on the surface of the steel specimen which has the highest and lowest stress. The MSC Nastran code was used to simulate the stress distribution on the U-bend steel specimen subjected to elastic/plastic strain. Boundary element method was applied to obtain the potential and current distribution on the surface of the U-bend type steel specimen due to the galvanic effect. The result shows that corrosion rate of the carbon steel was affected by the magnitude of the elastic and plastic strain working on the steel. In addition, the bigger magnitude of the elastic or plastic strain working on the steel the higher the corrosion rate. In corrosive environment, the effect of galvanic will occur on the steel surface with different magnitude of the elastic or plastic strain. The area on the steel surface which has biggest magnitude of the elastic or plastic strain becomes the most anodic area and becomes the easiest area to be attacked by corrosion. REFERENCES 1. Aoki S, Amaya K, Miyasaka M. Boundary Element Analysis on Corrosion Problems. Shokabo, Tokyo, 1998 (in Japanese). 2. Adey RA, Niku SM. Boundary element simulation of galvanic corrosion - the story of a major success for boundary element method. Boundary Element X, Vol. 2: Fluid Flow and Electrical Application, Computational Mechanics Publications, Springer-Verlag, 1988. 3. Fontana MG, Greene ND. Corrosion Engineering, 2nd edition, McGraw-Hill International, 1983.
— 191 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan,China ©2006 Tsinghua University Press & Springer
Simulation on Vortex Effect for Superconducing Devices Siu-Long Lei, Man I Lao *, Iat-Neng Chan Department of Electrical and Electronics Engineering, University of Macau, Macau, China Email: [email protected] Abstract The simulation of vortex dynamics motion in superconductor is based on the time-dependent Ginzberg-Landa equations in the non-equilibrium state. Runge-Kutta's method is used for time stepping and finite difference method is for space derivative during the simulation for the effects of applied magnetic field, vortex motion and material defects. In the research, simulation for several special electronic devices are accomplished for functional test. At least one design has been compared with measurement data in a real circuit. Major characters of simulation result are analyzed and reflected the reality of the notable phenomena as Meissner effect, penetration depth, coherent length and pinning force of superconductivity. There are two major objects have been done in the simulations. One is for the modification on the electric field and the magnetic field. The other is for the material properties of superconductivity. One interested subject is about the field slightly lower than the critical field He. The vortex movement during non-equilibrium state of the surface superconductivity is studied. The primary result show that the superconductivity near the surface is fluctuated and the central part is forming small vortex clusters. The relation between vortex fluctuation with material property and applied field is also investigated. REFERENCES 1. Gaitan F. Microscopical analysis of the nondissipative force on a line vortex in a superconductor. J. Phys.: Condens. Matter, 1995; 7(12): L165-L170. 2. Du Q, Gunzburger MD, Peterson JS. Analysis and approximation of the Ginzbrug-Landau model of superconductivity. SIAM Review, 1992; 34(1): 54-81. 3. Lele Sanjiva K. Compact finite-difference schemes with spectral-like resolution. Journal of Computational Physics, 1992; 103: 16-42.
— 190 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Special Hybrid Multilayer Finite Elements for 3-D Stress Analyses Around Quasi-Elliptic Hole in Laminated Composites Z. S. Tian**, Q. P. Yang \ X. Q. Zhang 2 1
Department of Mechanics, Graduate School, Chinese Academy of Sciences, P.O.Box 2706, Beijing, 100080 China Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing, 100080 China Email: [email protected] Abstract Two kinds of 3-dimensional assumed stress hybrid multilayer finite elements — one contains a traction-free planar surface and the other contains a traction-free cylindrical surface — have been developed based on the Hellinger-Reissner principle and a modified complementary energy principle respectively. The combination of these two kinds of special elements can be used for efficient and accurate analysis of stress around quasi-elliptic hole in thin to thick laminated composites. The expressions of fully 3-dimensional stresses of the special elements are derived, such that the homogeneous equilibrium equations in each layer, the continuity of the transverse stresses on the interlayer surface and the traction-free boundary conditions over the designated surfaces are satisfied a prior, while the interelement reciprocity traction condition is satisfied a posterior in a variational sense. All components of displacement are included since bending/stretching coupling may occur. The transverse-shear deformation effects are incorporated in each layer with displacement continuity enforced along interlayer surface. Example solutions have indicated that the combination of these special multilayer finite elements is far superior in predicting the distributions of circumferential stresses and transverse stresses for laminated composites with quasi-elliptic hole when very coarse element meshed are used. Meanwhile these special elements possess much more efficiency than the ordinary assumed stress finite elements and the conventional assumed displacement elements. REFERENCES 1. Tian ZS, Liu JS, Ye L, Pian THH. Studies of stress concentration by using special hybrid stress elements. Int. J. Num. Meth. Engng., 1997; 40(8): 1399-1412. 2. Tian ZS, Zhao FD. Stress concentration in a solid with symmetric U-shaped grooves. Strain Analysis, 2001; 36(2): 211-217. 3. Tian ZS, Zhao FD, Tian Z. Special hybrid stress element for stress analyses around circular cutouts in laminated composite. Scienc in China (Series E), 2001; 45(5): 531-541.
— 252 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanyo, Hainan, China ©2006 Tsinghua University Press & Springer
Static and Dynamic Testing of the SATUOeiras Viaducts M. Xu *, L. O. Santos, J. Rodrigues Department of Structures, National Laboratory for Civil Engineering, Lisbon, Portugal Email: [email protected] Abstract The first phase of SATUOeiras (Automated System of Urban Transport of Oeiras) was inaugurated in May 2004 (fig.l). The system consists of a single rail track that runs above ground level, on specially built viaducts, with fully automated vehicles moving along the track. At the 1st phase the system is 1260 m long, with three stations and two connecting viaducts between them. The viaducts VI and V2, with 33 m spans, have a length of 360 m and 460 m, respectively. A prefabricated solution was adopted for their construction[l]. Before the opening for traffic, static and dynamic tests were carried out on the viadutcs. The static test was performed with the train which was loaded up to a total of 197.9 kN. This train was placed in accordance to the load plan to obtain the maximum moments at the middle spans and check the behaviour of the joints between the prefabricated beams. Vertical displacements and rotations were measured during the static tests. The structural behaviour of the viaducts was also analysed with three dimensional finite element models (fig.2) [2]. A good agreement between experimental values and analytical results has been obtained. The dynamic tests consisted in ambient vibration measurements and tests with the train crossing the viaducts with different speeds. The ambient vibration tests were carried out in nine set-ups. During these tests 15 accelerometers were used. Sampling rate was selected as 1000 Hz. The software ARTeMIS was used for the modal identification [4]. The enhanced frequency domain decomposition technique (EFDD) was applied to estimate natural frequencies, mode shapes and the modal damping. The vibration modes obtained by the tests were compared with the calculated ones.
Figure 1: SATUOeiras
Figure 2: Finite element model of the viaduct VI
REFERENCES 1. Camara J, Rocha J, Cardoso D. SATUOeiras cable railway system. Struct. Eng. Int., 2005; 15(2): 82-84. 2. CSI. SAP2000 - Integrated Finite Element Analysis and Design of Structures, 2000. 3. Structural Vibration Solution - ARTeMIS Extractor Handy, Release 3.1, Denmark, 2002. — 238 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X.Aug. 21-23, 2006, Sanya, Hainan,China ©2006 Tsinghua University Press & Springer
Stress Intensity Factor of a Wide Range of Semi-Elliptical Partly Through-Wall Crack in a Finite-Thickness Plate K.P.Kou* Department of Civil and Environmental Engineering, University of Macau, Macao, China Email: [email protected] Abstract In practice, cracks of any awkward shape initiated accidentally, e.g. fabrication errors, exist in structures such as offshore steel structure. Existing of these flaws could lead to disastrous accidence due to fatigue effect. Therefore, a safe interval of maintenances is substantial in order to keep a reliable residual life and strength of the structure. To assess the fatigue effect, one approach is to make use of the stress intensity factor(SIF) of the cracks in facture mechanics. These flaws are usually treated as semi-elliptical surface cracks(with a and c as the minor and major axis) on the member of the structure e.g. BS7910. For plates with semi-elliptical surface crack, Newman, Raju and Kou have reported the stress intensity factor. However, for plates with partly through-wall cracks, namely an semi-elliptical crack with an imaginary crack depth a which is greater than the thickness (T) of the plate, the stress intensity factor was not reported. In the current work, semi-elliptical partly through-wall cracks (of sizes 1.0
*h
\
Figure: A 3D model with partly through-wall crack REFERENCES 1. Raju IS, Newman JCJr. Stress-intensity factor for a wide range of semi-elliptical surface cracks in finite-thickness plates. Engineering Fracture Mechanics, 1979; 11: 817-829. 2. Kou KP. The SIF for long-deep semi-elliptical surface crack in finite thickness plates. Proc.ABAQUS User Conference, Stockhom, 2005.
— 197 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X,Aug. 21-23, 2006, Sanya, Hainan,China ©2006 Tsinghua University Press & Springer
Structural Dynamic Reliability of Solid Rocket Motor Grains Shujun Zhang*, Junguo Ren College of Aerospace and Material Engineering, National University of Defense Technology, Changs ha, 410073 China Email: [email protected] Abstract Analytical methods to predict the stochastic response of MDOF-system are quite limited [1]. In fact numerical procedures, such as Monte Carlo simulation (MCS) techniques are the only available methods to treat practical reliability problems. Direct Monte Carlo simulation, however, requires a substantial amount of computer time and resources. Variance reduction techniques such as importance, directional, etc, are utilized to increase the efficiency of Monte Carlo simulation for analysis of complex dynamical system. This paper proposes an efficient simulation procedure for stochastic analysis of nonlinear dynamical systems with multi-degree freedom, namely rocket solid motor grains, based on Monte Carlo simulation. A simple criterion is established for indicating the importance of each dynamical response sample. According to this criterion, Russian Roulette & Split (RRS) method is applied to deal with the selected samples. The efficiency of this algorithm is much higher than that of direct MCS while the number of response samples in the low probability regions is increased. Then, structure dynamic reliability of grains was analyzed based on Monte Carlo viscoelastic stochastic finite element method. On the basis of nearly incompressible viscoelastic deterministic finite element method, this efficient simulation procedure was applied to increase the efficiency on account of the inefficiency of direct Monte Carlo simulation. Considering the randomness of internal press when motor starts, reliability and its variational trend of the solid rocket motor grain under internal pressure was analyzed in combination with failure criterion and minimal transform. In one numerical example, this procedure is compared with direct MCS demonstrating comparable accuracy and universal, thus suitable for engineering application. REFERENCES 1. Pradlwarter HJ, Schueller GI. On advanced Monte Carlo simulation procedures in stochastic structural dynamics. International Journal of Non-Linear Mechanics, 1997; 32(4): 735-744. 2. Pradlwarter HJ, Schueller GI, Melnikov PG. Reliability of MDOF systems. Probabilistic Engineering Mechanics, 1994; 14: 235-243. 3. Harnpornchai N, Pradlwarter HJ, Schueller GI. Stochastic analysis of dynamical systems by phasespace-controlled Monte Carlo simulation. Computer Methods in Applied Mechanics and Engineering, 1999;168:273-283.
— 208 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Studies of 4-node Membrane Element with Analytical StiffnessMatrix Based on the Quadrilateral Area Coordinates* YuDu 1 *, SongCen 1 ' 2 1
School ofAerospace, Tsinghua University, Beijing, 100084 China Failure Mechanics Laboratory, Tsinghua University, Beijing, 100084 China Email: [email protected], [email protected] 2
Abstract The new Quadrilateral Area Coordinate (QAC) method is a powerful tool to construct 2D finite element models [1]. Compared with the traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion. Various elements based on QAC method have been successfully developed, among which the 4-node quadrilateral membrane element AGQ6-I is a typical one [2]. Theoretically, by using the area integral formulae [3] the analytical stiffness-matrix could be obtained, which may greatly benefit the computation procedure. However, as the derivation of the analytical expression is relatively complicated, all the papers by far still adopt the numerical integration method for computer coding, which indeed impedes the advantages of the QAC method. So in this paper, by introducing the basic QAC formulae into two famous symbolic computation softwares, Maple and Mathematica, the analytical expression of the stiffness-matrix of AGQ6-I is obtained for the first time. Then a corresponding FORTRAN subroutine is compiled. Numerical examples show that the present scheme exhibits excellent performances in computation efficiency when compared with the QAC element using numerical integration and the isoparametric element. Furthermore, some general remarks for simplification are also concluded from the derivation process, which may provide significant reference for other researches. REFERENCES 1. Long YQ, Li JX, Long ZF, Cen S. Area coordinates used in quadrilateral elements. Commun. Numer. Meth. Engng., 1999; 15(8): 533-545. 2. Chen XM, Cen S, Long YQ, Yao ZH. Membrane elements insensitive to distortion using the quadrilateral area coordinate method. Computers & Structures, 2004; 82(1): 35-54. 3. Long ZF, Li JX, Cen S, Long YQ. Some basic formulae for area coordinates used in quadrilateral elements. Commun. Numer. Meth. Engng., 1999; 15(12): 841-852.
* This study was supported by the Natural Science Foundation of China (10502028), the Special Foundation for the Authors of the Nationwide (China) Excellent Doctoral Dissertation (200242).
— 251 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan,China ©2006 Tsinghua University Press & Springer
Study on the Criterion of In-plane Instability of Non-reinforced U-shaped Bellows Ye Chen*, Boqin Gu College of Mechanical and Power Engineering, Nanjing University of Technology, Nanjing, 210009 China Email: [email protected] Abstract In-plane instability is a type of plastic failure of non-reinforced U-shaped bellows. The instability will not only reduce the load-carrying ability and the thermal compensation capacity but also decrease the fatigue lifespan of bellows expansion joints. A study on the in-plane instability mechanism of non-reinforced U-shaped bellows under internal pressure or internal pressure-axial displacement is carried out by theoretical analysis, nonlinear finite element method (FEM) and experiments. The results indicate that whether bellows are stable or distorted mostly depends on the generation and propagation of the plastic regions. The in-plane instability critical loads can be obtained by calculating the stress distribution of the plastic regions and analyzing the propagation of the plastic regions both in the roots and the circular plates of bellows. The results obtained by theoretical analysis are in good agreement with experimental data. The now frequently used criterion of in-plane instability is based on the hypothesis of the generation of the plastic hinges both in the roots and crowns, and it may not be applicable to the bellows under the combined loads of internal pressure and axial compression. Based on the results obtained in this paper, a new criterion of in-plane instability of the U-shaped bellows is put forward. a 8000 Cl 7500 ? 7000' £ 6500 & 6000 tn 5500 . g 5000 g 4500 "£j 4 0 0 0 C 3500 ~ 3000 > 2500 g . 2000 §1500
- RZ10-300BI - RZ10-150BI
"
13 1000 jg
P
.5 CT,
500
> ^ + -
°
-500
3
5
8
m
l.&X.
~ *
10 13 15 18 20 23 25 28 30
The node number along longitude from root to crown of convolution Figure: Distribution of equivalent elastic stress in some bellows obtained by FEM REFERENCES 1. EJMA. Standards of the Expansion Joint Manufacture Association. New York, EJMA, 1993. 2. Broyles RK. Bellows instability. ASME PVP, 1989; 168: 37-43. 3. Hu Jian, Guo Bingliang et al. In-plane instability of U-shaped bellows subjected to pressure loadings. ASME PVP, 1992; 51: 229-240. — 210 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Suppression of Zero-Energy Modes in Hybrid Finite Elements via Assumed Stress Fields Canhui Zhang*, Dongdong Wang, Jianlin Zhang Department of Civil Engineering, Xiamen University, Xiamen, 361005 China Email: [email protected], [email protected], [email protected] Abstract For hybrid finite elements, if an assumed stress field does not contain enough appropriate stress modes, the resulting element will include zero-energy deformation modes and thus can not be used for pratical applications [1-3]. On the other hand, adding extra stress modes will require more computational effort. For a finite element including n degrees of freedom and r rigid body modes, generally m-n-r stress modes are considered to be the optimal choice from the computational point of view. However, so far there still does not exist a universal and rational way to derive the m optimal assumed stress modes that can be used to generate a hybrid element free of zero-energy or kinematic deformation modes. This paper present a methodology to suppress the zero-energy mode in hybrid element using assumed stress fields. The m basic deformation modes of hybrid element are derived straightforward from the displacement field, which are linearly independent to each other so that they can represent any deformation modes of given element. Their corresponding stress modes are employed to determine the zero-energy modes in the hybrid element. It is shown that a basic deformation mode is a spurious kinematic mode if its corresponding stress mode is orthogonal to all modes in the assumed stress field, and a assumed stress mode is zero-energy mode when it is orthogonal to all basic deformation modes. Based upon the orthogonality relationship between the initial stress modes and the basic stress modes that are corresponding to the basic deformation modes, one can find the necessary m stress modes to formulate a hybrid element free of hour-glass modes. The iso-function method is adopted here to derive the initial stress modes and a related systematic procedure is discussed. Furthermore, it is found that the zero-energy stress modes cannot suppress the zero-energy deformation modes, instead they increase the stiffness associated with the nonzero-energy deformation modes of the element. Thus it is not appropriate to include the zero-energy stress modes into the assumed stress field. The examples of 2-D, 4-node plane element and 3-D, 8-node solid element are provided to illustrate the proposed method. REFERENCES 1. Wu CC, Pian THH. Incompatible Numerical Analysis and Hybrid Finite Element Method. Science Press, Beijing (1997). 2. Pian THH, Chen DP. On the suppression of zero-energy deformation models. Int. J. Numer. Meth. Eng., 1983; 19: 1741-1753. 3. Zhang C, Feng W, Huang Q. The stress subspace of hybrid stress element and the diagonalization method for flexibility matrix H. Applied Mathematics and Mechanics, 2002; 23: 1263-1273.
— 254 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X,Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
The Dynamic Analysis of Main Building of Hangzhou International Conference Center H. J. Song*, Y. F. Luo, C. L. Xu,, M. W. Yang College of Civil Engineering, Tongji University, Shanghai, 200092 China Email: [email protected] Abstract Hangzhou International Conference Center is a high-rise steel building. Its structure is much complex. The main structure of the building is a sun-shaped braced-frame structure. Lots of curved beams, slanting columns and struts are adopted in the structure. Plane arrangement of the members is extremely complex. Horizontal and vertical stiffness vary greatly. Since the irregularity of the structure, the spectrums are much dense. The calculation of dynamic responses is much complicated. The coupled Reaction of different modes is much apparent. The response spectrum method and time-history method are both used to analyze the dynamic characters and seismic response of the complicated main building in this paper. The dynamic characters of the structure are obtained. The capability of seismic resistance is also calculated. It is a valuable reference for design of this structure and similar structures.
Figure 1: Finite element model of main building
Figure 2: Deformation shape under earthquake action
REFERENCES 1. ATC. Seismic evaluation and retrofit of concrete buildings. Report No. ATC-40, Applied Tschnology Council, Redwood City, California, USA, 1996. 2. Leger P, Ide IM, Paultre P. Multiple-support seismic analusis of large structures. Computer and Structures, 1990; 36 (6): 1153-1158.
— 224 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan,China ©2006 Tsinghua University Press & Springer
The Solutions of Stress and Displacement Fields of Orthogonal Anisotropic Plate with Edge-Cracks Z.R.Tian*,Z. Sun, Z.Y.Li Department of Mechanics, Northwestern Polytechnical University, XVan, Shaanxi, 710072 China Email: [email protected] Abstract To solve the stress-field {o^} and the displacement-field {«,} in the orthotropic plate with edge-crack, the authors established a particular method based on the concept of equivalent-space. The singularity of Kelvin solution of orthogonal anisotropic plate with crack has been using the virtual displacement method of Boundary Element Method. The Fourier transform and the basic solution of Laplace equation on the variables x and y, we could get the expressions of the stress-field {cr^} and displacement-field {w;} in the 1/4 plane(jt>0,j>>0), which are with the coefficients C(£)and D(n). In order to obtain the coefficients C(£)and D(TJ) in the integral equations which satisfy the boundary conditions, it need to solve Weber-Schafheitlins discontinuous integral equation, Bessel's and Abel style integral equations, the main problem is solving the Abel integral equation, and it can be done by transforming the Abel integral equation to the second kind Fredholm integral equation. From the solving of the second kind Fredholm integral equations, by using the third order B-Spline BjA(t), we can get the correlative coefficients a(t) and b(t) of the C(£)and D(TJ), then we have the C(£)and D(rj) to get the solutions of the {cr } and the {w,}. Thus, stress field and displacement field have also been solved. Final numerical solutions are obtained by C programming. The entire solving method is intricate, but precise in logic.
— 203 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
The State-of-the-Art Methodology to Compute the 3-D Stress Intensity Factors for Arbitrary Shaped Cracks in Complex Shaped Structures H. Okada1*, G. Yagawa2, H. Kawai3, K. Shijo4, D. Fujita4,Y. Kanda5, T. Fujisawa5, T. Iribe 5 Department of Nano-structure and Advanced Materials, Kagoshima University, 1-21-40 Korimoto, Kagoshima, 890-0065 Japan Center for Computational Mechanics Research, Toyo University, 2-36-5 Hakusan, Bunkyoku, Tokyo 112-8611, Japan Department of System Design Engineering, Keio University, 3-14-1 Hiyoshi, Kohokuku, Yokohama 233-0051, Japan 4 Technostar Co., Ltd., M21 Bldg., 2-2-5, Roppongi, Minatoku, Tokyo 106-0032, Japan Prometech Software, Inc., Sangakurenkei-Plaza, 4F, 7-3-1 Hongo, Bunkyoku, Tokyo 113-0033, Japan Email: [email protected] Abstract In present research, engineering softwares that can perform highly efficient and accurate fracture analyses based on the finite element method (FEM) is being developed. The developed softwares will drastically shorten time and labor cost to perform the fracture mechanics analyses. Structural integrity problems have been recognized as the major concerns by engineers in power plant, civil engineering, aerospace and ship-architectural industries. One of the scenario leading to structural failure is that (1) cracks from in the structure, (2) they propagate through the structure under the applied stress and (3) unstable crack propagation lading to catastrophic structural failure occurs. In this scenario, it is very important to detect the structural defects by non-destructive inspection (NDI) techniques and to predict how the existing cracks propagate through the structure. Thus, the remaining service life of damaged structure can be predicted. The major tool to perform the residual life prediction analysis is the finite element method (FEM). Once FEM analysis is performed for the damaged structure, fracture mechanics parameter such as the stress intensity factor is evaluated and it characterizes the severity of crack tip deformation field. Rate and direction of crack propagation are predicted based on the stress intensity factor. In this research we aim at developing softwares that can automate the fracture mechanics analysis by coupling the (1) automatic mesh generation software, (2) finite element program for large scale analysis and (3) a new virtual crack closure-integral method (VCCM) [1] for evaluating the stress intensity factor based on tetrahedral finite elements. Among them the VCCM technique is the key technology. In the presentation, the VCCM for quadratic tetrahedral finite element is described first and the-state-of-the-art mesh generation software called VENUS [2] and the use of free mesh method (FMM) [3] are discussed. REFERENCES 1. Okada H, Araki K, Kawai H. Stress intensity factor evaluation for large scale finite element analyses (virtual crack closure-integral method (VCCM) for tetrahedral finite element), submitted to Transactions of Japan Society of Mechanical Engineers (JSME), 2006. 2. Yagawa G. Node-by-node parallel finite elements: a virtually meshless method. Int. J. Numer. Meth. Engng., 2004; 60: 69-102. 3. WWW page of Technostar Co., Ltd., Japan, http://www.e-technostar.com/english/ — 200 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Thermally Induced Mechanical Changes around a Potential Nuclear Waste Repository in China Y. M. Liu lj2 *, J. Wang2, M. F. Cai \ S. R. Wang3 1
University of Science and Technology Beijing, Beijing, 100083 China Beijing Research Institute of Uranium Geology, Beijing, 100029 China China University of Geosciences Beijing, Beijing, 100083 China Email: [email protected] 2
Abstract Deep geological disposal is considered to be the best option to isolate the high-level radioactive waste (HLW) from the biosphere. Heat generated from the waste in the repository will result in an increase in rock temperature and substantially change the stress state of the host rock surrounding a nuclear waste repository. For the safe design of a deep underground HLW repository, there has to be a systematic consideration of all thermal, hydrological and mechanical effects that could prejudice the integrity of the repository and its man-made and natural barriers in the short and long terms [1]. The Beishan area in Gobi desert in Gansu province is considered as the most potential candidate area for HLW geological repository in China [2]. A numerical investigation is conducted on the impacts of the thermal loading history on the evolution of mechanical response of a fractured rock mass containing a hypothetical HLW repository in Beishan. The geological data are extracted from the site investigation results at Jiujing section, Beishan area. The large-scale far-field analysis is conducted using FLAC2D for coupled thermo-mechanical process. The results show that the temperature distributions at different time scales and the thermal stresses of fractured rock masses vary significantly with mechanical properties determined at the representative scale. Vertical heaving and horizontal tensile displacement are observed above the repository. This study provides an important base for site selection and repository design of HLW repository in China. REFERENCES 1. Hudsona JA, Stephansson O, Andersson J, Tsang CF, Jing L. Coupled T-H-M issues relating to radioactive waste repository design and performance. International Journal of Rock Mechanics & Mining Sciences, 2001; 38: 143-161. 2. Wang J, Chen W, Su R, Fan H. Studies on Geological Disposal of Radioactive Waste in China. Atomic Energy Science and Technoloty, 2004; 38(4): 339-342.
— 245 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanyo, Hainan,China ©2006 Tsinghua University Press & Springer
Using Finite Element Program Generator to Solve N-S Equation S. Wan1*, M.P. Nielsen2, G. Chai * 1
Transportation College, Southeast University, Nanjing 210096, China Department of the Civil Engineering Technical University of Denmark Email: [email protected] 2
Abstract The operator splitting method is used to deal with the N-S equation, in which the physical process described by the equation is decomposed into 2 processes: a diffusion process and a convection one. They are analyzed separately. Diffusion equation is solved first, and then the result is used in the solution of the convection equations. The virtual work equation of the diffusion equation is made. According to the standard FE assembling process, its FE equation is obtained. The mixed interpolation method in which the velocity field in the element is describe by shape function of the isoparametric element with 9 nodes and the pressure field is described by the interpolate function of the 4 nodes at the vertex of the isoparametric element with 9 nodes. The subroutine of the element and the integrated FE code are generated by the Finite Element Program Generator (FEPG) successfully. The lid-driven cavity problem is analysed. The physical parameters of the liquid in the cavity are: p = 1.0kg/m3 , ju = 10"3 kg/m • s .The boundary conditions in the lid-driven cavity problem are veloity on the surface on the cavity is zero excepte the top surface.The velocity along the top surface is given as a contant value. The grid is generated by software Gid. Mesh is also graded near the wall using a geometrical progression.The multi-frontal solver is used to solve the FE equation.Time increment is At = 0.01 sec and total time is 30 sec.The solution is used to compare with results of reference paper. The component in x direction of velocity distribution in the cavity along vertical centre-line,stream-function contour and the pressure contour calculated for Reynolds number Re=1000 are given.The solutions follow the results of reference paper very well.
— 179 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X,Aug. 21-23, 2006, Sanya, Hainan,China ©2006 Tsinghua University Press & Springer
VCCM Rule-Based Meshing Algorithm for an Automatic 3D Analysis of Crack Propagation of Mixed Mode Kohei Murotani**, Kanda Yasuyoki2, Toshimitsu Fujisawa2, Genki Yagawa * 1
Center for Computational Mechanics Research (CCMR), Toyo University, 2-36-5, Hakusan, Bunkyo-ku, Tokyo, 112-0001, Japan Prometech Software, Inc., Tokyo, Japan Email: [email protected] Abstract An analysis of crack propagation using FEM need to perform re-meshing for an updated shape of crack with each cycle. In an analysis of crack propagation of 3D mixed mode, the shape of crack seems to be complex. In addition, we must effectively calculate parameters of fracture mechanics and exactly forecast a direction of crack propagation. Because of this situation, we can analyze an automatic 3D analysis of crack propagation of mixed mode, if we can perform meshing satisfied the two basic conditions of VCCM (Virtual Crack Closure Method) for an arbitrary shape of crack. In this paper, we show an algorithm of a VCCM rule-based meshing for the arbitrary shape of crack and calculation results.
Figure: A crack propagation using FEM.
REFERENCES 1. Okada Hiroshi, Higashi Mayumi, Kikuchi Masanori, Fukui Yasuyoshi, Kumazawa Noriyoshi. Three dimensional virtual crack closure-integral method (VCCM) with skewed and non-symmetric mesh arrangement at the crack front. Engineering Fracture Mechanics, 2005; 72: 1717-1737. 2. Okada H, Kamibeppu T. A virtual crack closure-integral method (VCCM) for three-dimensional crack problems using linear tetrahedral finite elements. CMES: Computer Modeling in Engineering & Sciences, (accepted for the publication). — 199 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X,Aug. 21-23, 2006, Sanya, Hainan,China ©2006 Tsinghua University Press & Springer
Wave Propagation in Orthotropic Elastic Shells: Theoretical and Numerical Modeling B. Tie*, D. Aubry Laboratoire de Mecanique des Sols, Structures, et Materiaux (CNRS UMR 8579), Ecole Centrale Paris, Grande Voie des Vignes, 92295 Chatenay-Malabry Cedex, France Email: [email protected], [email protected] Abstract Shell type structures are used in a wide variety of industrial components, especially in automotive or aeronautic industries. A full understanding and predictive modeling of elastic waves propagation through those structures can be of great importance at their design stage for several reasons, such as the noise reduction in a vehicle or the control of high energy shock waves triggered by pyrotechnic cut in a space launcher. This paper deals with the theoretical and numerical modeling of elastic wave propagation in shells. The aim is to discuss the relevance of theoretical models and to develop appropriate and efficient numerical tools. Orthotropic elastic shells are considered in this paper and the classical Mindlin shell kinematics is used to model them. First theoretical analyses developing the acoustic tensor are presented, in order to highlight the role played by the shell curvature in the transmission, reflection and conversion phenomena of membrane and flexure waves. Dispersion equations are discussed in the case of cylinder or cone shells. Then in the case where high frequencies are involved and the shortest wavelength is smaller than the shell thickness or the local curvature radius, the relevance of the Mindlin kinematics and its enriched variants is discussed. Besides, the theoretical analyses are always compared to and enhanced by the numerical modeling performed using a space-time Galerkin discontinuous solver. Estimates of model errors are also numerically evaluated to quantify differences between the considered shell kinematical models. Finally, several numerical results on shell type industrial structures are presented. REFERENCES 1. Batra RC. Plane wave solutions and moda analysis in higher order shear and normal deformable plate theories. Journal of Sound and Vibration, 2002; 257(1): 63-88,. 2. Tie B, Aubry D, Boullard A. Adaptative computation for elastic wave propagation in plate/shell structures under moving loads. European Revue of FEM, 2003; 12(6): 717-736. 3. Tie B, Aubry D, Grede A. Numerical modeling of elastic wave propagation in honeycomb sandwich panels under moving loads: application to space launcher. 6th International Symposium on Launcher Technologies, Munich 8-11, Nov. 2005.
— 209 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan ,China ©2006 Tsinghua University Press & Springer
A Novel Fuzzy expert Diagnosis System of Inner-Faults for ThreePhase Squirrel Cage Induction Motors Tak Son Cheang*, Si Leong Chan, Booma Devi Sekar, Ming Chui Dong Faculty of Science and Technology, University of Macau, P.O. Box 3001, Macau, China Email: [email protected], [email protected] Abstract Three phase induction motors are widely used in industrial production all over the world. Due to high utilization rate, frequent starting and changing load condition, the appearance of failures in induction motors is relatively high. A sudden fault will cause large economic losses. Therefore, the early fault detection becomes very important. During practical operation of three-phase induction motors in industry, the inner faults may occur-in their rotor and stator windings. These kinds of faults will make serious influence on the operation of the motor. There is insufficient R&D in the diagnosis system of inner-faults of squirrel cage induction motor. Thus a new research on the fuzzyexpert diagnosis system of inner-faults for three-phase induction motors is presented. The purpose of fault diagnosis is to isolate the cause of a system malfunction in a timely manner. This paper presents a new sequence performing diagnosis of the three-phase induction motors as: sample the fault symptoms, carry the fuzzyexpert forward & backward inference, deduce the fault hypotheses and conclude the fault discrimination. Among them, a novel technique of how to define the various membership functions and the relevant fuzzy sets concerning the uncertainty issues based on the symptoms of motor faults (experimental, simulation & calculation data), and how to construct the proper inference nets for producing the production rules are explained. In summary, the following issues will be presented in this paper: 1. List of all faults of motor with related symptoms and hypotheses; 2. Expert's knowledge about the priori probabilities of each fault and the combinational faults of the motor; 3. Definition of fuzzy sets concerning the uncertainty symptoms & hypotheses; The inference nets with all necessary parameters for further calculating the probability propagations. Finally, a series of experiments of diagnosing the stator and rotor faults are shown.
— 258 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanyo, Hainan, China ©2006 Tsinghua University Press & Springer
Damage Detection of Vibrating Structure from Limited Natural Frequencies X. L. Li l*, H. Okuda \ G Yagawa2 1
Research into Artifacts, Center for Engineering, The University of Tokyo, Chiba, 277-8568 Japan Center for Computational Mechanics Research, Toyo University, Tokyo, 112-8611 Japan Email: [email protected]
2
Abstract Conventional non-destructive structural damage detecting approaches, such as eddy current, ultrasonic, and radiographic testing, the location of the damage must be known a priori or the whole structure needs to be tested. The vibration-based method uses changes in natural frequencies to detect damage and can avoid the above limitations. In mathematics it is proven that if all natural frequencies are known the stiffness matrix of structural system can be reconstructed fully, but in practice only limited natural frequencies are available, so we only can pursue the least squares solution of it. Accurate Jacobian matrix in each iterative step is necessary to solve this ill-posed underdetermined inverse eigenvalue problem by the Newton's method. In this paper, the Jacobian matrix of reconstruction equation is evaluated accurately and efficiently by the proposed symbolic-numerical hybrid approach. The numerical results of fixed-free spring-mass system show that good results can be obtained even only limited measured natural frequencies are used with different damage scenarios.
VW\_{
p V W q
]
AAAA_ .
^/v'VVV.^
]
Figure: Fixed-free spring-mass system
REFERENCES 1. Friedland S, Nocedal J, Overton ML. The formulation and analysis of numerical methods for inverse eigenvalue problems. SIAM J. Num. Anal., 1987; 24(3): 634-667. 2. Chu MT. Inverse eigenvalue problems. SIAM Review, 1998; 40(1): 1-39. 3. Chen Xuzhou, Chu MT. On the least squares solution of inverse eigenvalue problems. SIAM J. Num. Anal., 1996; 33(6): 2417-2430.
— 260 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Updating Noise Parameters of Kalman Filter Using Bayesian Approach K. I. Hoi *, K. V. Yuen, K. M. Mok Department of Civil and Environmental Engineering, University of Macau, Macau SAR, China Email: [email protected] Abstract Kalman filter [ 1 ] is known to be a robust tool in state estimation for linear or slightly nonlinear systems in diverse disciplines of science and engineering. In the area of structural engineering, Kalman filter has also received enormous attention over the years due to its importance for model updating, response prediction, structural control and health monitoring. The algorithm becomes popular since it provides not only the state estimation but also the associated uncertainty of the estimation. In addition, the algorithm is online so that the state vector is immediately updated once a new data point is obtained. However, the accuracy of Kalman filter depends on the prior knowledge of the process noise and measurement noise parameters, which is difficult to be obtained in practice. In the present study, the Bayesian propabilistic approach [2] is proposed to estimate these noise parameters in the Kalman filter for the case when the input is a zero-mean Gaussian white noise process and limited output measurements are available. The optimal estimates of the noise parameters are chosen by the maximum likelihood criterion. Through the two illustrative examples, the estimated noise parameters are close to the actual values in the sense the actual parameters are located in the region with significant probability density. Therefore, it is concluded that the Bayesian approach is able to provide accurate estimates of the noise parameters, and hence the state estimation, for Kalman filter. REFERENCES 1. Kalman RE. A new approach to linear filtering and prediction problems. Transactions of ASME, Journal of Basic Engineering, 1960; 82: 35-45. 2. Beck JL, Katafygiotis LS. Updating models and their uncertainties, I: Bayesian statistical framework. Journal of Engineering Mechanics, 1998; 124: 455-461.
— 259 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
3D Animation for Free Mesh Method Shinsuke Nagaoka!*, Masakazu Inaba2, Genki Yagawal 1
Center for Computational Mechanics Research (CCMR), Toyo University, 2-36-5, Hakusan, Bunkyo-ku, Tokyo, 112-0001, Japan 2 Techno Star, Inc., Tokyo, Japan Email: [email protected] Abstract In recent years, the performance of computer has been improved dramatically. Numerical or computation technology is also developing greatly with the above improvement in the performance of computer. On the other hand, the objects for the analysis become more and more complicated. To deal with the large-scale and complex problems, new approach called the meshless method has been actively studied. The Free Mesh Method is one of the meshless methods, which can solve the complicated phenomenon that the body is dynamically fragmented. In order to animate such an analysis result, this paper describes the 3D animation system for the free mesh method, which is intended to be a post-processor for dynamic phenomena.
REFERENCES 1. Yagawa G, Yamada T. Free mesh method: a new meshless finite element method. Comp. Mechanics.l8:383-386,1996.
— 263 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
A Stabilized Conforming Integartion Procedure for Galerkin Meshfree Analysis of Thin Beam and Plate Dongdong Wang* Department of Civil Engineering, Xiamen University, Xiamen, 361005 China Email: [email protected] Abstract This paper aims to develop an efficient Galerkin meshfree formuation to analyze thin beam and palte. First, through a reformulation of the reproducing conditions (or consistency conditions), a meshfree double-variable approximation based on both the deflection and slopes is constructed. It is shown that this approximation can approximate a given function with better accuracy than that purely based on the deflection variables. Then with this meshfree approximation function, the Galerkin framework for thin beam and plate is formulated. To treat the essential boundary conditions in the Galerkin meshfree formulation, the transformation method [ 1 ] is generalized herein to relate the nodal deflection and rotation coefficients and their corresponding physical values of deflection and rotations. Since the weak form of thin beam and plate involves the 2nd order derivatives, accurate numrical integration for the discrete stiffness matrix requires intensive computational effort. In this study, numerical tests show that low order Gauss quadrature as well as the previous stabilized conforming nodal integration [2-4] which was developed to integrate the stiffness with 1st order derivative, can not fully stabilize the mnumerical solutions. To obtain the pure bending solution and remain spatial stability, the srain smoothing idea in the stabilized conforming nodal integration is extended here. Rather than diectly employing the nodal strain smoothing and nodal integration, the problem domain is partitioned into integration cells and the numerical integration is carried out on several sampling integration points defined in each integration cell. At the smapling points, the curvature smoothing is performed within conforming sub-cells which comprise of the integration cell. Due to the conforming nature of curvature smoothing, the resulted meshfree scheme can exactly reproduce bending solutions. Numerical examples demonstrate the present strategy has superior convergence rates, accuracy and efficiency, compared with that using higher order Gauss integration. REFERENCES 1. Chen JS, Pan C, Wu CT, Liu WK. Reproducing kernel particle methods for large deformation analysis of nonlinear structures. Comput. Meth. Appl. Mech. Engng., 1996; 139: 195-227. 2. Chen JS, Wu CT, Yoon S, You Y. A stabilized conforming nodal integration for Galerkin meshfree methods. Int. J. Numer. Meth. Eng., 2001; 50: 435-466. 3. Wang D, Chen JS. Locking-free stabilized conforming nodal integration for meshfree Mindlin-Reissner plate formulation. Comput. Methods Appli. Mech. Eng., 2004; 193: 1065-1083. 4. Wang D, Dong SB, Chen JS. Extended meshfree analysis of transverse and inplane loading of a laminated anisotropic plate of general planform geometry. Int. J. Solids Struct., 2006; 43: 144-171.
— 264 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug 21-23, 2006, Sanyo, Hainan, China ©2006 Tsinghua University Press & Springer
Element-Free Galerkin method with wavelet basis Y. H. Liii *, Y. N. Liu, Z. Z. Cen Department of Engineering Mechanics, Tsinghua University, Beijing, J 00084 China Email: [email protected] Abstract Many numerical methods have been developed and used to solve problems of computational mechanics. Recently, one of the hottest topics in computational mechanics is the meshless or meshfree method. Some meshless methods have been proposed and achieved remarkable progress, such as the element-free Galerkin (EFG) method [1], the meshless local Petrov-Galerkin (MLPG) methods [2],and so on. In above-mentioned meshless methods, it is key and necessary to construct the so-called shape function, which is complicated, time-consuming and even hard to realize in some special conditions. Furthermore, the complexity of shape function will increase computational cost in total process. It is desirable to find a new method, which is simple and reasonable to construct shape functions in meshless method. However, it seems to be a difficult task. So we should resort to some other mathematical tools. Wavelet is a powerful tool in solving many problems in science and engineering. In recent years, there has been an increasing interest in the wavelet-based approach due to the success in wavelet-based methods in several applications. Some of recent investigations on the wavelet method include papers by many scholars such as Amaratunga and Williams [3]. This paper is aimed at introducing a new meshless method by using DB wavelet. In the construction of shape function, scaling function in wavelet analysis is directly employed as shape function to approximate the unknown field functions. Because of the compact support and orthogonality, DB wavelets can describe the details of the problem conveniently and accurately. The other advantage brought by compact support is that the DB wavelet-based meshless method has relatively small degrees of freedom in solving practical problems. Compared with traditional meshless methods, this method is concise in formulations, and flexible in applications. The numerical examples illustrate that the DB wavelet-based meshless method has high computational accuracy. So DB wavelet-based meshless method has enormous potential in the analysis of other complicated problems. REFERENCES 1. Belytschko T, Lu YY, Gu L. Element free Galerkin methods. Int. J. Numer. Methods Engrg., 1994; 37: 229-256. 2. Alturi S N, Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput.Mech.Engrg.,1998; 22: 117-127. 3. Amaratunga K, Williams JR. Wavelet-Galerkin solutions of boundary value problems. Comput. Mech. Engrg., 1997; 4: 243-285.
— 265 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Error Estimations in LBIEM and Other Meshless Methods H. B. Chen1+, D. J. Fu \ X. F. Guo 2 , P. Q. Zhang ! CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui, 230027 China 2 Teaching and Research Section of Mechanics, Dalian Jiaotong University, Dalian, 116028 China Email: [email protected] Abstract: Error estimation in numerical computations relates to the reliability of algorithms and improvement of computational efficiencies. Large amounts of relevant research have been developed and the most classes of error estimators are residue-based and recovery-based in FEM [1]. In meshless methods, nodes can be easily moved, added and deleted; therefore it leads to more convenient and attractive to implement adaptivity processes [2, 3]. In the current paper, the developments of error estimation in meshless methods are firstly reviewed. Some schemes to define the a-posteriori error estimators are quoted in detail. For instance, In EFGM, the stress projection technology, the strain gradient method, the cell energy method, recovery based estimation technology, etc, are respectively adapted to obtain the referenced solutions. Then, based on the relevant ideas of FEM and the other meshless methods, the dual error indicators defined by the differences of three sets of solution are introduced for the local boundary integral equation method (LBIEM) [4]. The three sets of potential solution are: "Original" denotes the potential calculated by MLS through the fictitious values at original nodes; "Taylor" denotes the potential obtained by MLS using Taylor series expansion, for the newly added nodes; "Refresh" denotes the potential calculated by MLS through the fictitious values at the original and newly added nodes, after a reanalysis of the LBIEs has been performed. The following figures show that, for the newly added nodes, the "Taylor" errors are always lower than their "Original" ones; in the well-distributed arrangements, the "Refresh" errors are similar to the "Taylor" ones at the newly added nodes. As a result, when these two defined error indicators are consistent with each other, the nodal arrangement with new additional nodes is well-distributed; otherwise, modulate the location and number of the new additional nodes. REFERENCES 1. Zienkiewicz OC. The background of error estimation and adaptivity in finite element computations. Comput. Meth. Appl. Mech. Eng., 2006; 195: 207-213. 2. Gavete L, Cuesta JL, Ruiz A. A procedure for approximation of the error in the EFG method. Int. J. Numer. Methods Eng., 2002; 53(3): 677-690. 3. Liu GR, Tu ZH. An adaptive procedure based on background cells for meshless methods. Comput. Meth. Appl. Mech. Eng., 2002; 191: 1923-1943. 4. Guo XF, Chen HB. Dual error indicators for the local boundary integral equation method in 2D potential problems. Eng. Anal. Bound. Elem., (in press).
— 261 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X,Aug. 21-23, 2006, Sanya, Hainan,China ©2006 Tsinghua University Press & Springer
Parallel Computing for Enriched Free Mesh Method (EFMM) Yosuke Kobayashi *, Genki Yagawa Center for Computational Mechanics Research (CCMR), Toyo University, 2-36-5, Hakusan, Bunkyo-ku, Tokyo, 112-0001 Japan Email: [email protected] Abstract Performed in this paper is a structural analysis by the Parallel Free Mesh Method, which is a kind of mesh-free method. In order to improve the accuracy of the solution by the Free Mesh Method, we have developed the Enriched Free Mesh Method, where the displacement field and the strain field are independently assumed. The unknown parameters of these fields are determined by employing the Hellinger-Reissner principle. Some parallel performance study is made with a cluster computer. REFERENCES 1. Aoyama Y. A Guide to parallel programming: MPI version. RIKEN Information Base Center, 2004. 2. Yagawa G, Yamada T. Free mesh method: a new meshless finite element method. Int. J. Computational Mechanics, 1996; 18: 383-386.
— 262 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
3D BEM for Piezoelectric Solids of General Anisotropy M. Denda1*, C.-Y Wang 2 ' 3 1
Mechanical and Aerospace Engineering Department, Rutgers University, NJ 08854-8058, USA Mathematics and Modelling Department, Schlumberger-Doll Research, CT 06877-4108, USA 3 {currently on secondment to) Department of Engineering Mechanics, Tsinghua University, Beijing, 100084 China Email: [email protected], [email protected] 2
Abstract In this paper we present a new scheme of three-dimensional boundary element method for the general anisotropic piezoelectric solids. We use the Radon transform representation of the three-dimensional fundamental solutions of piezoelectricity and integrate them analytically over the triangular boundary element with the linear interpolation. This reduces the computation for the system matrices G and H from the standard singular surface integrations to the simple regular line integrations and enables a drastic reduction of the computation time. The integrand of the line integral consists of the product of a function dependent and another function independent on the location vectors representing the source and observation points. The latter function depends only on the material and element properties and thus need be calculated only once for each element and saved for a repeated use in the calculation of G and H matrices and in the post-processing. Exploitation of this favorable structure results in the further reduction of the computation time for very large systems. The implementation of the proposed method with numerical examples will be presented. REFERENCES 1. Denda M, Wang CY, Yong YK. 2-D time-harmonic BEM for solids of general anisotropy with application to eigenvalue problems. J. Sound Vibrat., 2003; 261: 247-276. 2. Wang CY, Achenbach JD, Hirose S. Two-dimensional time domain bem for scatteringof elastic waves in solids of general anisotropy. Int. J. Solids Structures, 1996; 33(26): 3843-3864. 3. Denda M, Araki Y, Yong YK. Time-harmonic BEM for 2-D piezoelectricity applied toeigenvalue problems. Int. J. Solids Struct., 2004; 41: 7241- 7265. 4. Wang CY. Elastic fieldelds produced by a point source in solids of general anisotropy. J. Engng. Math., 1997; 32(1): 41-52. 5. Chen T, Lin FZ. Boundary integral formulations for three-dimensional anisotropic piezo-electric solids. Computational Mechanics, 1995; 15: 485-496. 6. Pan E, Yuan FG. Boundary element analysis of three-dimensional cracks in anisotropicsolids. Int. J. Numer. Meth. Engng., 2000; 48: 211-237.
— 270 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Analysis of Quantum Dots Induced Strain and Electric-Field in Piezoelectric Semiconductor Substrate of General Anisotropy C.-Y. Wang **, M. Denda2, E. Pan 3 1
Mathematics and Modelling Department, Schlumberger-Doll Research, CT 06877-4108, USA, {currently on secondment to) Department of Engineering Mechanics, Tsinghua University, Beijing, 100084 China 2 Mechanical and Aerospace Engineering Department, Rutgers University, NJ 08854-8058, USA 3 College of Engineering, University of Akron, Akron, OH 44325-3905, USA Email: [email protected], [email protected], [email protected] Abstract Characteristics of the self-organized quantum dots (QDs) such as electron and hole energy levels and wave functions are dependent to the state of strain and electric field produced during the growing process of QDs in a semiconductor substrate. The calculation of the strain and electric field is one of the most challenging components in the QDs simulation process. It involves material anisotropy induced coupling between the elastic and electric fields and it must include the full three-dimensional and usually intricate shapes of the QDs. Numerical simulations are often performed by finite difference, finite element, or atomistic techniques, all require substantial computational time and memory. In this paper, we present a new Green's function approach which takes into account QDs of arbitrary shape and semiconductor substrates with the most general class of anisotropy and piezoelectricity. Following the literature of micromechanics, the problem is formulated as an Eshelby inclusion problem of which the solution can be expressed by a volume-integral equation that involves the Green's functions and the equivalent bodyforce of eigenstrain. The volume integral is subsequently reduced to a line integral based on exploring a unique structure of the Green's functions. The final equations are cast in a form that most of the computation results can be repeatedly used for QDs at different locations - a very attractive feature for simulating large systems of QD arrays. The proposed algorithm has been implemented and validated by comparison with analytical solutions. Numerical simulations are presented for pyramidal QDs in the substrates of Gallium Arsenite (GaAs) [001] andGaAs[lll].
Figure: Micrograph of pyramid-shaped quantum dots grown from indium, gallium, and arsenic. Each dot is about 20 nanometers wide and 8 nanometers in height. Image courtesy NIST.
— 271 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanyo, Hainan, China ©2006 Tsinghua University Press & Springer
Computer Simulation of Quantum Dot Surface under Stress Xiaoming Liu, Zhuo Zhuang *, Tong Zhang School ofAerospace, Tsinghua University, Beijing, 100084 China Email: [email protected] Abstract In thin film structure, a traction-free quantum dot surface is usually under large stress for the presence of misfit strain between substrate and film. Such kind of material surface becomes unstable and roughens. The surface perturbation will rapidly lead to the breaking up of the coat, and the films eventually become damaged. In this paper, a variational formulation is proposed to study the evolution of the stressed quantum dot structure. Surface diffusion is considered as the dominant mass transport mechanism, while mass transport will be significant when process has the features of severe working condition such as relatively high stress, high temperature, electric current, small size scale. The elastic field was obtained by the first-order perturbation solutions. In our approach, the surface shape is expanded in terms of a complete set of basis functions, and surface governing equations can be obtained by the principle of minimization of energy. Our simulations reveal that surface profile grows due to the destabilizing influence of the large stress effects and shrinks due to the stabilizing influence of small stress effects. The competition between elastic strain energy and surface energy can lead to the growth of surface profile perturbations at large stress, small surface tension. The misfit strain between film and substrate can significantly influence the surface evolution. 006 Surttc* tvotulton profltM
005
(A 0j
004
t =0.0001)00
003
t"«0.002908
t'=0.000442 t*=0.009X28
^3 02 001
-001 "VV*Q
~ " " ~ 0.2
04
08
0.8
1
y/X
Figure: Evolution of quantum dot surface
REFERENCES 1. Liu P, Zhang YW, Liu C. Computer simulations of the Stranski Krastanov growth of heteroepitaxial films with elastic anisotropy. Surface Science, 2003; 526: 375-382. 2. Yang WH, Srolovitz DJ. Cracklike surface instabilities in stressed solids. Physical Review Letters, 1993; 71: 1593-1596. 3. Shenoy VB, Ramasubramaniam A, Freund LB. A variational approach to nonlinear dynamics of nanoscale surface modulations. Surface Science, 2003; 529: 365-383. — 269 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Molecular Dynamic Simulations of CNT-Water Nanostructures J. Zou 1*, X. Q. Feng \ B. Ji \ H. Gao 2 1
Department of Engineering Mechanics, Tsinghua University, Beijing, 100084 China Division of Engineering, Brown University, 182 Hope Street, Providence 02912, USA Email: [email protected] 2
Abstract We report discoveries from molecular dynamics simulations that single-walled carbon nanotubes (CNT), with different diameters, lengths, and chiralities, can coaxially self-assemble into multiwalled carbon nanotubes in water via a set of consecutive spontaneous insertion of smaller tubes into larger ones. The assembly process is tube-size dependent and the driving force is primarily the inter-CNT van der Waals (vdW) interactions. Such coaxial self-assembly suggests possible "bottom-up" routes for fabrication of novel nanodevices. After the assembly, typical water structures besides bulk phase include a one-dimensional water chain inside the small tube, a uniform or non-uniform water shell between the two tubes and a "boundary layer" of water near the exterior wall of the large tube. We found that a concentric water shell consisting of one to three layers of water molecules can form between the two selected CNTs, which lead to a class of carbon-water-carbon composite nanotubes with distinct lifetimes. Analysis of the potential energy of the CNT-water system indicates that the carbon-water-carbon composite nanotubes are stabilized by both the tube-water and intertube van der Waals interactions, and a minute change in the CNT-water attraction will dramatically affect the stability of such composite nanotubes. Our results have general implications on filling nanoporous materials with nanoparticles or tubular nanostructures via the nonspecific, nonbonding vdW interactions. REFERENCES 1. Gao H, Kong Y, Cui D, Ozkan CS. Spontaneous insertion of DNA oligonucleotides into carbon nanotubes. Nano Lett., 2003; 3: 471-473. 2. Zou J, Ji B, Feng XQ, Gao H. Self-assembly of single-walled carbon nanotubes into multiwalled carbon nanotubes in water: molecular dynamics simulations. Nano Lett, 2006; 6: 430-434. 3. Zou J, Ji B, Feng XQ, Gao H. Molecular dynamics studies of carbon-water-carbon composite nanotubes. Small, (in press).
— 268 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Molecular Dynamics Simulation of Length Size Effect on Mechanical Properties of Nano-Metal D. Huang*, J. S. Zhuo Department of Engineering Mechanics, Hohai University, Nanjing, 210098 China Email: [email protected] Abstract Based on embedded atom potential and molecular dynamics method, a numerical simulation model suitable for analysis of mechanical properties and behavior of nano-scale metal was proposed. With this model the failure process and mechanical properties of nanocrystalline nickel wires with different cross section sizes were studied. Simulation reveals the motion of atoms, appearance and growth of nano-scale voids, changes of atomic arrangements and relationships between average atomic stress, energy and crystal lattice strain in nano-scale metal wires under static external load. Numerical results show that initial unstable energy, as a result of free surfaces and surface reconstruction, takes large effects on the deformation and failure mechanism of nano wires. Energy in surface atoms is much higher than that in the inner ones, so surface atoms depart from standard crystal lattice positions and nano voids come into being along the surfaces firstly. The deformation process of nano wire behaves as the expansion and connection of nano cavities from surface into inner lattices, which agrees well with experimental phenomena. What's more, the elastic modulus, yield and fracture strength on definite lattice directions of nickel nano wires with different cross section sizes were obtained, and the length size effect of nanocrystalline metal on mechanical properties was analyzed further. According to simulation results we put forward two calculation formulae on elastic modulus, yield strength and fracture strength of nickel nano wire. In the first one, elastic modulus and yield strength of metal nano wire are both linear to the logarithm of cross section length size, but fracture strength has an inverse relation to exponential cross section length size. In the other one, the elastic modulus and yield strength are divided into three parts: the contribution from corner lattices, surface lattices and inner ones, with different volume ratio and effect factor. Two formulae can predict the elastic modulus, yield strength and fracture strength of a nanocrystalline nickel nano wire according to the cross section size or surface lattice ratio respectively, and keep remarkable accordance with simulation results.
REFERENCES 1. Broughton JQ, Meli CA, Vashishta P, et al. Direct atomistic simulation of quartz crystal oscillators: bulk properties and nanoscale devices. Physical Review B, 1997; 56: 611-618. 2. Liu WK, Karpov EG, Zhang S, et al. An introduction to computational nanomechanics and materials. Computer Methods in Applied Mechanics and Engineering, 2004; 193: 1529-1578. 3. Voter AF, Chen SP. Accurate interatomic potentials for Ni, Al, and NisAl. Materials Research Society Symposium Proceeding, 1987; 82: 175-182.
— 267 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
The Numerical Prediction of Effective Properties of Non-Continuous Carbon Nano-Reinforced Composites by the Macro-Microscopic Homogenization Method Dongmei Luo **, Wenxue Wang2, Yoshihiro Takao2, Koichi Kakimoto2 1
Environment and Civil Engineering School, Foshan University, Guangdong, 528000, China Research Institute for Applied Mechanics, Kyushu University, 816-8580, Japan Email: [email protected]
1
Abstract In this paper, the homogenization method with exact periodic boundary conditions is adopted to predict the effective stiffness of composites reinforced with straight and sinusoidal wavy Carbon Nano-Tubes (CNTs) as shown in Figure (a) and (b), which are considered as the effective discontinuous transverse isotropic short fiber. Numerical calculations for regular and staggered array models (Figure (c)) are performed by using the commercial finite element software ABAQUS. Comparing with those from Mori-Tanaka and Halpin-Tsai theories, it is found that the stiffness of CNTs composites are not only related to aspect ratio and CNTs volume fraction as described in the above theories, but also to depend on CNTs arrays and distribution within the selected Representative Volume Element (RVE). The results from the two empirical approaches are included in the present results with special spacing ratios of horizontal and vertical fiber ends (Tf lHf ), and staggered arrays are significant to predict the effective stiffness with a high degree of axial overlap of fibers. For wavy CNTs reinforced composites, it is found that the CNTs waviness results in the reduction of effective stiffness of composites compared with straight CNTs reinforcement. The degree of reduction is dependent on the waviness amplitude, CNTs arrays method and wavy CNTs distributions. The results prove that the macro-micro homogenization method is efficient to predict the effective stiffness of a CNTs-composite by considering more microscopic parameters such as the CNTs properties, geometry characteristic and CNTs dispersion in the matrix, simultaneously.
^ m m m ^ ^ ^ ^ a ^ ^ ^ . ^
v
'
.. .. ,,...„ ; +* «*> * * m l * » t pmnm at *»«v»*r»«* array lor
mF^
(a) (b) (c) Figure: Straight and sinusoidal wavy CNTs, and regular and staggered array models REFERENCES 1. Luo DM, Wang WX, Takao Y, Kakimoto K. Prediction of the stiffness and stresses for carbon nano-tube composites based on homogenization analysis. Reports of Research Institute for Applied Mechanics, Kyushu University, Japan, 2005, No. 129, pp. 37-45. 2. Liu YJ, Chen XL. Evaluations of the effective material properties of carbon nanotube-based composites using a nanoscale representative volume element. Mechanics of Materials, 2003; 35: 69-81. — 266 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X,Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
A Note on the Complexity of the PCG Algorithm for Solving Toeplitz Systems with a Fisher-Hartwig Singularity Seak-Weng Vong *, Wei Wang, Xiao-Qing Jin Department of Mathematics, University of Macau, Macao, China Email: [email protected], [email protected] Abstract Recently, Y. Lu and C. Hurvich showed that the complexity of T. Chan's preconditioned conjugate gradient algorithm for solving the Toeplitz system Tn (f)x = b is o(«log 3 «) where the generating function/is given by f(co) = \l-e^[2d
h(co)
with de(-^9 ^)\{0} and h(a>) being positive continuous on [~n, x] and differentiable on [-TZ, 7r]l{0}. Although their results are interesting, there exist some improper expressions in their proofs needed to be corrected. In this paper, we try to improve those improper expressions and demonstrate these important results by some numerical tests.
REFERENCES 1. Chan R, Ng M. Conjugate gradient methods for Toeplitz systems. SIAM Review, 1996; 38: 427-482. 2. Jin X. Developments and Applications of Block Toeplitz Iterative Solvers. Kluwer Academic Publishers, Dordrecht, and Science Press, Beijing, 2002. 3. Lu Y, Hurvich C. On the complexity of the preconditioned conjugate gradient algorithm for solving Toeplitz systems with a Fisher-Hartwig singularity, SIAM J. Matrix Anal. Appl., 2005; 27: 638-653.
— 277 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
A Parallel Computing Method of Object-Oriented FEM Based on Substructure* H. M. Zhao *, K. Zhang, Z. Z. Dong Department of Mechanics, College of Science, China University of Mining & Technology, Xuzhou, Jiangsu, 221008 China Email: [email protected] Abstract The method of object-oriented programmer is combined with the parallel computation of FEM in this paper. Based on the usual substructure method in FEM, a substructure class is established. Its objects automatically generate their meshes with given precision because it consists of the member function which is able to generate meshes automatically according to the data of boundary nodes. This is really significant in practice since people may require different precisions in different substructures. With the realization of the parallel class of MPI in C++ program environment, the previous serial object-oriented tools, such as development, debug and other software, can still be used. It is more important that the method of class libraries has the better expansibility and transplantation. So the design of parallel programmer is easier. Having designed the parallel computation steps of the object-oriented FEM based on substructure, the author calculates the problem of rectangular beam as an example and analyzes the efficiency of these programs. It shows that the method has more flexibility and the efficiency will be higher with the increase of the number of substructures. REFERENCES 1. Mackie RI. Object-oriented programming of the finite element method. International Journal for Numerical Methods in Engineering, 1992; 35: 425-436. 2. Yuan ZQ, Zhong SS. Sub-structural method of FEM by the object-oriented program. Journal of Chongqing University (Natural Science Edition). 2001; 24(3): 35-37 (in Chinese). 3. Zhang JF, Jiang HD. Performance analysis in FEM substructure parallel algorithm. Mechanics in Engineering, 2002; 24(5): 35-37 (in Chinese).
* This work is supported by the Science and Technology Foundation of China University of Mining & Technology. — 280 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X,Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Adaptive Under-Frequency Load Shedding Scheme by Genetic Algorithm Chinwang Lou *, Mingchui Dong, Chikong Wong Faculty of Science and Technology, University of Macau, P.O. Box 3001, Macau, China Email: [email protected], [email protected], [email protected] Abstract Under-Frequency Load Shedding (UFLS) is one technique used in the power industry for many years. The UFLS function is to rescue the system under extreme disturbances and avoid the system collapse. Traditionally, a scheme is designed based on the projected scenarios (considering the summer and winter conditions) as well as the worst generation deficiency that could occur in the system. Usually, when the old UFLS settings are no longer appropriate to the new operating mode, they must be re-designed. I.e. based on the past experience in design and operation, the new scheme and settings are assumed firstly. Then, off-line computer simulation is adopted to verify the UFLS performance. Settings are adjusted according to the simulation result. Afterwards, the simulation and performance are verified again under the adjusted settings. This procedure is repeated until the settings are sought such that the UFLS demonstrates the best performance on the selected scenarios. Many efforts were devoted to simplify this procedure. In this paper, a novel adaptive load shedding method based on Genetic Algorithm (GA) is proposed to automate the findings of optimal settings such that the repetitive trial-error can be minimized greatly. The simulation results on figures show that the new scheme based on GA has superior performance, compared with old scheme. Average Load shed Amount
Avg. Frequency Performance
I Old Dg60-4
I Old Dg60-4
4.50 s? 2.50 1.50 0.50
|—^
100.0
rlTrMl.1T.B-,. T :
%
Scenario
r
-
^
i° m\ 11 11
^
III1
Scenario
Figure: The performance comparison in two load shedding schemes (g60-4=settings optimized by GA) REFERENCES 1. Prasetijo D, Lachs WR, Sutanto D. A new load shedding scheme for limiting underfrequency, IEEE Transactions on Power Systems, 1994; 9(3): 1371-1377. 2. User guide of MTSP (mid-term stability program), Tsinghua University, Beijing, China. 3. Al-Hasawi WM, El Naggar KM. Optimum steady-state load-shedding scheme using genetic based algorithm. IEEE Melecon 2002, Cairo, Egypt, May 7-9, 2002. — 272 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
An Effective Computer Generation Method for the Domain with Random Distribution of Large Numbers of Heterogeneous Grains Yan Yu l *, Junzhi Cui 2 , Fei Han l Department of Applied Mathematics, School of Science, Northwestern Poly technical University, XVan, 710072 China 2 Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100080 China Email: [email protected], [email protected] Abstract In this paper in order to perform the prediction of the physics and mechanics properties for the composite materials with random distribution of large numbers of heterogeneous grains/cavities an effective computer generation method is presented to more perfectly and rapidly generate the samples of the random distribution domain with large numbers of grains/cavities. At first the heterogeneous geometries of grains/cavities are represented and the stationary random distribution with large numbers of grains/cavities is defined. In order to construct the algorithm for generating the samples of inhomogeneous stationary random distribution the selection algorithm with one stochastic variable is extended to the situation with several stochastic variables, and the selection theorem with several stochastic variables is stated. And then the detailed procedure of new algorithm is described. Finally several illustrations for 2 and 3 dimensional random distribution domains with the grains of different geometries are demonstrated respectively. The computer method in this paper is able to generate the sample with a higher percentage of grain volume and better stochastic property, and suitable to arbitrary stationary probability distribution model. The practice shows that the computer method in this paper is effective. REFERENCES 1. Li YY, Cui JZ. The computer simulated method for the domain with large numbers of random ellipse grains/cavities and the improved automatic generation triangle mesh algorithm. Chinese J. Comput. Mech., 2004; 20(3): 290-295 (in Chinese). 2. Wang ZK. Foundations and Application of Probability. Beijing Normal University Press, 1996 (in Chinese).
— 273 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
An Improved ICCG Method of Large-Scale Sparse Linear Equation Group* Y.J. Zhang*, Q. Sun School ofAeronautics, Northwestern Poly technical University, XVan, 710072 China Email: [email protected] Abstract In the field of engineering computation, many problems finally go to solve a large-scale linear equation group. Computational efficiency greatly relies on solving methodology and storing way of the equation group. This paper employs an improved ICCG (incomplete Cholesky conjugate gradient) method for improving the solving efficiency, and takes the fully sparse strategy for the storage of the sparse and symmetrical matrix of the equation group such that can save storing requirement to computer. Coefficient matrix of the linear equations is sparse and symmetrical. For the sake of CPU operational time saving to accesses data in matrix decomposition and reducing storing requirement to computer, we introduce fully sparse strategy structure that stores only nonzero elements of symmetrical part using chain pattern management. Apparently, its storing quantities are small, and its structure is convenient for research, insertion and deletion. When condition number of coefficient matrix is very big, coefficient matrix is morbid, and then iterative solution methods for sparse linear equations may be poorly convergent. Fortunately, appropriate preconditioning techniques can reduce condition number. In 1992, Saad introduced incomplete Cholesky decomposition with two thresholds One-threshold r controls magnitude of decomposed elements in every row. The other threshold p controls quantity of decomposed elements of every row. This method is denoted as ICCG (p9 r ) . Although ICCG (/?, r) is effective for symmetrical and positive definite matrix, some diagonal elements may be negative or quite small during incomplete decomposition. If diagonal elements are negative, preconditioned matrix may not be positive definite or approximate A well. If diagonal elements are quite small, they must bring big rounding errors, and then influence quality of decomposition and efficiency of solution. Therefore, we bring an improved diagonal method: Supposed that T is 1-norm or 2-norm of the / th row of preconditioning matrix, if diagonal element dn < T , then dti = T; otherwise don't modify the diagonal element. The improved ICCG (p,r) method can ensure quality of decomposition, thus improve the solving efficiency. Numerical examples show that the method is reliable and the high efficient.
REFERENCES 1. Wu JP, Wang ZH. Problems and improvements to the incomplete Cholesky decomposition with thresholds. Journal on Numerical Methods and Computer Applications, 2003; 3: 207-214. 2. St Georges P, Warzee G. High-performance PCG solves for FEM structural analysis. International Journal for Numerical Methods in Engineeing. 1996; 39:1313-1340 3. Beaumens R. Iterative solution methods. Applied Numerical Mathemetics, 2004; 51: 437-450. * This work is supported by the National Natural Science Foundation of China (No. 10477018). — 279 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan,China ©2006 Tsinghua University Press & Springer
One-Point Integration that Handles Shear-Locking in Cubic Splines Simon Wang **, Yingshun Zhang 2 Department ofAeronautical and Automotive Engineering, Loughborough University, Loughborough LE11 3TU, UK 2 School of Engineering, Coventry University, Coventry CV1 5FB, UK Email: [email protected] Abstract A layerwise cubic B-spline finite strip method is developed for free vibration analysis of laminated plates. Numerical tests show that the method can give accurate predictions for natural frequencies of moderately and truly thick plates. However, it encounters shear-locking difficulty when thin plates are considered. Studies reveal that conventional selectively reduced integration technique as used in FEM fails to remove the shear-locking, but discover that it can be completely eliminated by using an integration scheme such that one-point Gauss integration is used per spline section in the strip direction whilst the conventional selectively reduced integration scheme in the crosswise direction. With this approach, introduction of an extra constraint on transverse deflection is needed at the both ends of the strip. This approach is termed as LWB33-sFSM(SRI-lP) which has the capability to produce accurate predictions for natural frequencies of truly thin and thick isotropic and composite laminated plates. REFERENCES 1. Wang S, Dawe DJ. Vibration of shear-deformable rectangular plates using a spline function Rayleigh-Ritz approach. International Journal for Numerical Methods in Engineering, 1993; 36: 695-711. 2. Wang S, Dawe DJ. Vibration of shear-deformable beams and plates using spline representations of deflection and shear strains. International Journal of Mechanical Sciences, 1994; 36: 469-481. 3. Wang S. A unified Timoshenko beam B-spline Rayleigh-Ritz method for vibration and buckling analysis of thick and thin beams and plates. International Journal for Numerical Methods in Engineering, 1997; 40: 473-491.
— 278 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Prediction of Ambient PMio Concentration with Artificial Neural Network L. H. Lam *, K. M. Mok Department of Civil and Environmental Engineering, Faculty of Science and Technology, University of Macau, Macao SAR, China Email: [email protected] Abstract Previous studies with artificial neural network (ANN) application on air quality prediction show success even most models developed use only temporal data of air concentrations; hence mainly time series analyses are performed. It is known that the concentrations of air pollutants are highly related to the variations of the local and regional meteorology conditions which dictate the dispersion and transport routes of them. Many correlation studies and models simulating the fate and impacts of the released pollutants are these bases. Meanwhile, ambient air pollutants may also affect the concentrations of each other therefore making prediction or modelling of their behaviours a very complex problem. This study aims at designing economic and flexible ANN models for the 24-hour-ahead predictions on concentrations of respiratory suspended particulates (PMio) taking into account the effects from local meteorological conditions and related pollutants. The ANN applied in this study is a three-layer feed-forward network (TLFN) of the back-propagation type. To achieve computation efficiency, the size of the input data is limited to six parameters per input set. In addition, variation of the predicted hourly PMio concentration is assumed to depend only on meteorological and air quality conditions within the last 72 hours. With these as the main criteria, models for PMio concentration prediction are developed and tested with one year of hourly measured data in a small coastal city, Macao. The measured data include seven meteorological parameters (dew point, wind direction, wind speed, relative humidity, precipitation, sunshine hour fraction, and temperature) and concentrations of five criteria pollutants (PMio, SO2, NO/NO2/NOX, O3, and CO). Based on previous study, these data are divided into two seasons namely summer and winter due to the prevailing monsoon climate; hence the development of the PMio models for these two seasons are treated independently. Individual season segment of data is further divided into three sub-sets for model training, testing and validation purposes. To select the proper six input parameters for each seasonal model, correlation coefficients among the hourly concentrations of the listed pollutants and meteorological parameters are calculated. Six input parameters with the highest absolute values of correlation coefficients are selected to form the model input pattern with the minimum correlation coefficient value for cut-off being 0.73. The number of neurons used in the hidden layer for each model with its selected six-parameter input pattern is determined by systematic trials of minimum root mean square error. Five and six neurons are determined for the summer and winter models. The trained models are then used to predict PMio concentrations for seven days and compared with actual measurements. Absolute relative percentage error (ARPE) and mean absolute percentage error (MAPE) are used as comparison criteria. Results show that 75% of the predictions in both models achieve an accuracy of ARPE less than 30%, while 100% of the predictions in the winter model could achieve an accuracy of ARPE less than 40%. The overall MAPE for the two models are 49% and 77%, respectively. Overall, the developed ANN models can capture the general trends of the real measurement. Larger errors occur at those hours with high and sharp concentration peaks which may be considered as noises caused by instantaneous, individual incidents occurred in the vicinity of the monitoring station. These abnormal individual incidents may not be easily captured based on knowledge of the past. — 276 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Promotion of Frontier Science Research by Aid of Automatic Program Generation Technology B. X. Wu u * , H. S. Qian2, S. Wan3 1
Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing, 100080 China Beijing Fegen Software Company, Beijing, 100086 China 3 Southeast University, Nanjing, 210096 China Email: [email protected] 2
Abstract Based on a new DIY concept for software development [1], an automatic program-generating technology attached on a software system called as Finite Element Program generator (FEPG) provides a platform of developing software, through which a scientific researcher can submit his special physico-mathematical problem to the system in a more direct and convenient way for solution. The software execution manner is completely different with usual: In FEPG mode, a couple of files in a special language for describing both the partial differential equations to be solved and the solving algorithm and procedures should be prepared, in stead of importing parameters to solve partial differential equations in normal commercial software mode (see Figure 1). The calculating program is automatically generated by the system based on these files and then used to solve the problem. As an open platform, its flexibility greatly expand users' problem-solving ability, e.g. in integrating with new calculating algorithms and schemes, and in solving multiphysics problems. Two examples of numerical simulation are shown in this paper to illustrate the usage and superiority of automatic program generation technnology. Both are solved by using finite element method. For a thermo-elastic problem with non-Fourier heat conduction, implicit Newmark algorithm is adopted to solve the wave equations. For the simulation of the flow and heat transfer in a heat pipe, the solution of a typical multiphase, multi-zone and multi-physics problem is easily realized in a uniform manner. A lot of unique features of FEPG make it a powerful tool of numerical analysis for frontier sciences associated often with new physical models including novel constitutive equations and/or covering interactive multiphysics phenomena. Calculating scheme FEPG mode import
solution
Commercial software mode parameters
" W
bfa'Ckbox
solution
Figure 1: Different modes of software execution REFERENCES 1. Bangxian WU. How to cope with unknowingly coming software revolution? Software World, 2004; 5: 33 (in Chinese) — 281 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X,Aug. 21-23, 2006, Sanya, Hainan,China ©2006 Tsinghua University Press & Springer
Study on Displacement Prediction of Landslide Based on Grey System and Evolutionary Neural Network W.Gao* Department of Civil Engineering, Wuhan Polytechnic University, Wuhan, 430023 China Email: [email protected] Abstract Landslide is a very serious geological disaster. So, how to control the landslide has become a very important work. To control landslide disaster, the forecasting of landslide is a very powerful method. But the development of landslide is a very complicated dynamic system. To describe this system very accurately is very hard. But the measured displacement series can describe the general laws of landslide development. So, some methods for displacement prediction of landslide are proposed. From analysis of those methods, we can find that, the neural network is a good method. Generally, the displacement time series of the landslide can be divided into some sections, such as, even section, periodic section and fluctuant section, et al. For different section, the different method can be taken. In this paper, considering the monotonously increasing character of the displacement time series of the landslide, this time series is divided into two sections, such as, the trend section and the deviation section. Here, based on the principles of displacement decomposition, the trend of displacement time series is extracted by Grey System and the deviation of Grey System is approximated by the new ENN model. In this new ENN model, the architecture and algorithm parameters of neural network are evolved simultaneously through combining modified BP algorithm and Immunized Evolutionary Programming proposed by author. The Immunized Evolutionary Programming is the combination of traditional evolutionary programming with artificial immune system principles. Using the above analysis, a new intelligent prediction method is proposed here. At last, one engineering examples is used to verify calculating effect of the proposed method. Xintan landslide in China is a very famous landslide for its successful prediction. To control this landslide, a lot of measured displacement data are gotten. With those data, our new method is used to forecast the landslide. The results show that the generalization of the new method is good and it can predict the displacement of landslide very well. So, this new method can be used in real engineering practice very well. -Measured diaplacement -Computing displacement
,11 16 + time step
Figure: Measured displacement and computing displacement of Xintan landslide — 275 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
The Pseudo-spectral method and Matlab Implement* Songling Wang, Zhengren Wu*, Youliang Cheng School of Energy & Power Engineering, North china electric power university, Baoding,, 071003, China Email: [email protected] Abstract The pseudo-spectral method based on function approach is good for solving nonlinear equation. Because the surplus term in difference scheme sometimes can affect the computing result, thereby, the function approach method becomes a more popular one in the numerical simulation. Now, the pseudo-spectral method is the major one, for its small aliasing error. There are some kinds of language in solving the nonlinear equation, Matlab has been a good one in numerical computation and simulation, and it has been widely used in hydrodynamics and applied mathematics, etc. many complicated engineering problem can be solved by Matlab, and the numerical results can be showed by its excellent graphics. As a common spectral method, the pseudo-spectral method used spectral disperse (Fourier transform) treatment of the space dependence together with a difference scheme in time, then the derivatives (or other operations) are algebraic in the transformed variable. In the paper, for the leapfrog, the traditional Lax-Wendroff form was discarded, and the above pseudo-spectral method was adopted. As for the possibility of separation of the solutions between successive time levels, we adopted the averages of adjacent levels and restart the scheme from the new levels, so the precision can also be assured. At one time, the complex-valued problem in Fourier transform was treated by aliasing. For example, we solve the fKdV equation with pseudo-spectral method and draw the waterfall with Matlab, the results are shown in the Figure.
Figure: The numerical simulation results for fKdV equation REFERENCES 1. B.Fornberg, G. B. Whitham, A Numerical and Theoretical Study of Certain Nonlinear Wave Phenomena, J. Fluid. Mech, Trans R.Soc. London, 289, (1978), 333-404. 2. Yong Zhu, Resonant of Nonlinear Capillary-Gravity Waves, Phys. Fluids, 7, (1995), 2294-2296. 3. Ying Long Zhang,Song Ping Zhu. Subcritical, transctitical and superctitical flows over a step. J. Fluid Mech, 1997,333,257-271. * The project is supported by the National Natural Science Foundation of China (Grant No. 10272044), Research Fund for the Doctoral Program of the ministry of Education of China (20040079004) — 283 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Three-Dimensional Mesh Generation Using the Crossed Circle Method H. Suzuki *, Y. Ezawa Department of Computational Science & Engineering, Toyo University, Kawagoe, 850-8585 Japan Email: [email protected] Abstract Delaunay method is a representative method in FEM. The quality of mesh generation by this method, however, depends on the allocation of nodes. Crossed Circle Method (CCM) was developed for solving this problem. CCM is the method of two-dimensional mesh generation that allocates nodes in advance only on a domain boundary and adds nodes automatically in the inside of domain. In this research, we developed the program that generates mesh automatically with three-dimensional tetrahedron elements using CCM. In addition, we checked our program with some mesh generation. CCM is based on Delaunay method. In Delaunay method, the circumscribed circle of the triangle does not contain any other nodes. When nodes except vertexes are contained in the circumscribed circle, the diagonal line of the quadrangle made from two adjoining triangles is swapped. In this research, we developed three-dimensional CCM, for tetrahedron elements and we proposed the following algorithm. First, when nodes except vertexes are contained inside the circumscribed sphere of a tetrahedron in the three-dimensional Delaunay method, the nodes are swapped, as shown in Figure 1. Tetrahedron elements will increase in number from two to three. Second, circumscribed sphere is calculated for three tetrahedrons after the swap, respectively. Only when the center of the circumscribed sphere is included in both of remaining two circumscribed spheres, it is investigated whether the existing node is in the near. When there is no existing node, the center-of-gravity point of the triangle of which is the center of three circumscribed spheres is added. Figure 2 is the example of mesh created by three-dimensional CCM. Some numerical examples showed the validity of this method using developed program.
Figure 1: Swapping of tetrahedron elements
Figure 2: Mesh created by Crossed circle method
REFERENCES 1. Ezawa Y. Triangulation with internal points generated by crossed circles. WCCM VI in conjunction with APCOM'04, Sept. 5-10, 2004, Beijing, China. 2. Taniguti T. Auto Mesh Generation for FEM. Morikita, 1992 (in Japanese).
— 274 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanyo, Hainan, China ©2006 Tsinghua University Press & Springer
Uniformed NURBS Surface Deformation Subject to Boundary Conditions Kin Man Lo *, Zhixin Yang Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Taipa, Macau, China Email: [email protected] Abstract To allow mass custermization in competitive industries, it is important to conduct new product design and development with concentration on few key features while reusing the existed portion of design in terms of geometric shape and boundary condition. Partition methods will be firstly applied to separate a product model into a base shape and working feature. Customized design will be implemented by replacing the working feature with a new pattern, which shall be deformed such that the boundary is matched and the finallized feature is closed to the original one. This paper presents a new surface deforming method with an attempt to solve mentioned design problem. The control net of a surface is treated as a space truss so that the control points are considered as the nodes of the structure. When any of the nodes is moved, the entire structure is deformed accordingly. The techniques on the construction of the control net, determination of displacement of boundary node and unconstrainted node, and surface morphing will discussed in detail. Due to the localization property of NURBS surface, the number of control points could be adjusted is often restricted in traditional method. The proposed deforming method enables the control net being deformed gloabally and in a uniformed manner, which result a 'similar' deformed surface to the original pattern the designer intended to apply in the new product. It is believed the proposed method could be applied in related industries including shoe and car design. REFERENCES 1. Sanchez-Reyes J. A simple technique for NURBS shape modification. Computer Graphics and Applications, IEEE, 1997; 17: 52-59. 2. Hu S-M, Li Y-F, Ju T, Zhu X. Modifying the shape of NURBS surfaces with geometric constraints. Computer-Aided Design, 2001; 33: 903-912. 3. Dachille IX F, Qin H, Kaufman A. A novel haptics-based interface and sculpting system for physics-based geometric design. Computer-Aided Design, 2001; 33: 403-420.
— 282 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X,Aug. 21-23, 2006, Sanyo, Hainan, China ©2006 Tsinghua University Press & Springer
A 2-D Natural Element Model for Jointed Rock Masses Tiantang Yu*, Qingwen Ren Department of Engineering Mechanics, Hohai University, Nanjing, 210098 China Email: [email protected] Abstract According to the characteristic structural features of jointed rock masses, a natural element method (NEM) model is proposed for the mechanics analysis of jointed rock masses based on the Sibsonian interpolation or Laplace interpolation. In the model, the jointed rock mass is regarded as a system of intact rock blocks connected by discontinuous joints modeled by interfaces. The displacement field of each block is constructed by the natural neighbor interpolation. To deal with the discontinuities of rock masses, the displacement fields are constructed to be discontinuous between blocks. The displacement fields and their gradients are continuous in each block. Numerical simulations illustrate NEM has advantages of both element free method and finite element method, and does not have their disadvantages. The present method is developed for two-dimensional linear elastic analysis for jointed rock structures, and can be extended to three-dimensional and non-linear analysis.
— 292 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanyo, Hainan, China ©2006 Tsinghua University Press & Springer
A Study on Temperature Distribution in a Cross Section of Concrete Box Girder Bridge Yiping Tan *, Dajian Han Department of Civil Engineering, South China University of Technology, Guangzhou, 510640 China Email: [email protected] Abstract It is known that nonlinear temperature variation over a cross section of long-span continuous box-girder beam bridges or continuous rigid-frame box girder bridges can cause longitudinal stresses and that in some cases such kind of stresses may reaches or even exceeds those induced by the live loads and that temperature cracking may occur in the structure component. However, the mechanism of such phenomenon is not very clear yet. Therefore, to predict the stresses caused by temperature distribution is important for a correct design of the bridge structures. The purpose of the present paper is to present a practical computation method to simulate the temperature distribution over cross sections of a concrete box girder bridge. The relative factors considered include the bridge geometry, the geographical location, the bridge orientation, the material properties and ambient climatic conditions. In this paper heat flow equations over a concrete bridge cross section and heat boundary conditions of outside and inside the box-girder are first derived. And then numerical solution for daily time variation of air temperature is presented. The relationships between inside concrete temperature and ambient climatic conditions that include solar radiation, relative humidity, and wind speed etc. are established. A prediction for variation of concrete temperature is obtained. The results are compared to the observed values measured from The Guangzhou Guanyinsha Bridge that is a single-cell box-girder bridge. Finally, numerical method and computer programming are given to predict the temperature distribute in concrete bridge cross sections. This can be used to generate the thermal loads for finite element analysis.
r / -^-i '
-horizonal ovehang providing shade
surface exposed to sotar radiation 3
surface
Figure: Geometry defining incidence angle of solar radiation REFERENCES 1. Elbadry MM, Ghall A. Temperature variations in concrete bridges. Journal of Structural Engineering, ASCE, 1983; 109(10): 2355-2374. 2. Roberts-Wollman CL, Breen JE, Cawrse J. Measurements of thermal gradients and their effects on segmental concrete bridge. Journal of Bridge Engineering, 2002; 7(3): 166-174. — 286 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Advances in Unsaturated Soil Mechanics Zhankuan Mi *, Zhujiang Shen Nanjing Hydraulic Research Institute, Nanjing, 210024 China Email: [email protected]; [email protected] Abstract Most of soils above the groundwater level encountered in the engineering were in the state of non-stauration. The special soils such as loess, expansive soil and artificial fill were all typical unsaturated soils. Advances in unsaturated soil mechanics were lower than those in saturated soil mechanics. The restricted factors were as follows: 1. Testing technique was relatively not perfect. The test difficulties of unsaturated soil were as follows: (1) It was composed of solid phase, fluid phase, gas phase and contraction membrane. It was very difficult to measure the stress and deformation of the above four phases individually. (2) The suction value ranges from 0 kPa to 106 kPa. But it was very difficult to measure the matrix suction when its value was greater than 80 kPa. (3) As its permeability coefficient was small, the test duration was long. 2. Although it has been presented many constitutive relations such as elastic models, elastic-plastic models, damages models and thermo-mechanical models, the theoretical system of unsaturated soil was far immature. The new constitutive model should describe the reversible and irreversible change process along with the stress and suction change process. Advances in the measuring technology and constitutive model for unsaturated soil were comprehensively summed up. Some suggestions were proposed on the further research towards the application of unsaturated soil theories in engineering practice.
— 296 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Composite Construction in Reinforced Concrete Taking into Consideration the Non-Rigid Bond of Interfaces in Joints V. Lindig * Bonhoefferstr. 43, Weimar, 99427 Germany Email: [email protected] Abstract The meaningfully combination of various building materials is a fundamental component of modern con structions, the so-called composite constructions. As such, the recording of bond behavior in joints is a crucial factor to be considered in the design of load-bearing structures in respect of new building and retrofit. The behavior of the plain or reinforced concrete-concrete interfaces in joints taking into consideration potential effects such as various rough contact surfaces have a significant influence on structural behavior of complex reinforced concrete structures and composite constructions respectively. In contrast to the case of physically localized behavior, the behavior of the bond interfaces between old concrete and new concrete in joints under aspects of multi-parametered influential factors and how this influences the global structural behavior of composite construction raises issues which are still open contrary to research. A three-dimensional, physically non-linear continuum model has been developed on the basis of the finite element method. This enables the multi-parametered influence of the various surface structures and the reinforcement positioning of the concrete-concrete bond interface to be investigated discretely as a component part of complex composite constructions exemplary represented in figure. On the basis of the extensive simulation results [1], it can be proved, that the relevant European standard EC 2 do not reflect the realistic structural behavior. A novel differentiated design concept for concrete- concrete interface joints has been formulated and recommended therefore for the first time under consideration of relative displacements of the contact surfaces and with reference to the bearing structure [1].
t) flwjjrtnomwsiiufcf VWtaft&rw
t
Huff-J « Mrtwtfieli «nvt* t A AstmtiAqte Oct**WXOWMHI V\xnt
r) NwoukpannBiifUJintMl in VMwiidfeffwrhninff
() Akniwiw ichafckfi":»iVf YiMtiaflifiwwrltinifag
Figure: An exemplary rigid composite framework principle at the 3-d finite element analysis. REFERENCES 1. Lindig V. Numerical Simulation, Structural Analysis and Design of Composite Constructions in Reinforced Concrete taking into Consideration the Non-rigid Bond of Interfaces in Joints. Doctoral Thesis, Bauhaus-Universitat Weimar, Germany, Shaker Verlag Aachen, www.shaker.de (printed and online version), 2005 (in German). — 284 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Drag Forces Applied on Rock Matrix by Fluid Flow through Fracture Network in Rock Mass Junrui Chai 1 ' 2 * 1
College of Civil and Hydroelectric Engineering, China Three Gorges University, Yichang, 443002 China College of Hydroelectric Engineering, XVan University of Technology, Xi 'an,/T10048 China Email: [email protected] 2
Abstract It is very important to investigate the forces applied on the rock mass by the fluid flow through fractured rock mass, which is one of the issues for analyzing the stability of rock mass. The forces applied on the fissure walls by the fluid flow include the hydrostatic seepage pressure and the dynamic seepage pressure, i.e., the drag force. Based on the cubic law of the single fissure flow, the equations of the drag forces applied on the fissure walls by the single fissure flow are deduced by means of the momentum law of fluid mechanics. The equations are designated for the cases of no-filled fissure, filled fissure and the combined flow of fluid and the fillings, respectively. The equations have important values for analyzing the effect of fluid flow on the behavior of deformation and strength of fractured rock mass, and are the foundation of the interaction mechanism between stress and fluid flow. Based on the equations, the two kinds of forces applied on the fracture wall of fracture network in rock mass are studied, which include the normal hydrostatic seepage pressure and the tangent drag force. The equivalent node force of joint element is deduced under the two-dimensional and three-dimensional conditions. A numerical computation example is also given to indicate the effect of seepage through fracture network on the stress of rock mass. REFERENCES 1. Lewis RW, Schrefler BA. The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media, 2ndedn. John Wiley & Sons Ltd., Chichester, England, 1998. 2. Chai Junrui, Li Shouyi, Wu Yanqing. Multi-level fracture network model for coupled seepage and stress fields in rock mass. Communications in Numerical Methods in Engineering, 2004; 19(1): 63-74. 3. Chai Junrui, Li Kanghong, Wu Yanqing, Li Shouyi. Coupled Seepage and Stress Fields in Roller Compacted Concrete Dam. Communications in Numerical Methods in Engineering, 2005; 21(1): 13-21.
— 291 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Identification of Electric Conductivity and Impedance of Reinforced Concrete by Boundary Element Inverse Analysis Masato Yoshida **, Kazuhiro Suga 2 , M Ridha3, Shigeru Aoki 4 , Kenji Amaya5 1
GraduateSchool of Engineering, Toyo University, Japan Centerfor Computational Mechanics Research, Toyo University, 2-3 6-5 Hakusan, Bunkyo-ku Tokyo, Japan 3 Department of Mechanical Engineering, Syiah Kuala University, BandaAceh, Indonesia 4 Department of Computational science and Engineering, Toyo University, Japan 5 Department ofMechanical andEnviromental Informatics Tokyo Institute of Technology, 2-12-1 Ookayama, Meguroku Tokyo 152-8552, Japan Email: [email protected], {ksuga, ridha, saoki}@eng.toyo.ac.jp, [email protected] 2
Abstract Corrosion of steel bars in concrete is a major cause of failure of the reinforced concrete structures. Numerical inverse analysis is expected to become a useful tool for the corrosion detection. In this research, a new method is introduced for identifying the electrical conductivity of concrete and the impedance of steel-concrete interface by using some potential data which are measured on the concrete surface. The identification is based on the boundary element inverse analysis. The inverse analysis was carried out by minimizing the cost function, which is the different between measured and calculated potential in the concrete surface. Laplace equation, which is solved by boundary element method, is used to describe the potential in the concrete domain. An experiment using a concrete block with an embedded rebar is used to demonstrate the effectiveness of the proposed method. The alternative current is impressed into the concrete domain at one point on the concrete surface and the potential is measured at several points on the concrete surface. REFERENCES 1. Aoki S, Amaya K, Miyasaka M. Boundary Element Analysis on Corrosion Problems. Shokabo, Tokyo, 1998. 2. Press WH, Teukolsky SA,Vetterling WT, Flannery BP. Numerical Recipes in C\ Gijutsu Hyoron Co. Ltd., 1994 (in Japanese). 3. Ridha M, Amaya K, Aoki S. Improvement of AC impedance method for monitoring corrosion of rebar in concrete structure by boundary element method. Zairyo-to-Kankyo, 1999; 48(10): 654-659.
— 288 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanyo, Hainan, China ©2006 Tsinghua University Press & Springer
Numerical Implementation of a Bounding Surface Bubble Model for Structured Soils J. R. Maranha*, A. Vieira Department ofGeotechnics, Laboratorio Nacional de Engenharia Civil Av. do Brasil, 101 1700-066 Lisboa, Portugal Email: [email protected] Abstract In this work, the numerical implementation of a bounding surface model for structured soils formulated by Kawadas and Belokasfl] in the explicit finite difference code FLAC is described. This model incorporates capabilities to simulate soil destructuring, inherent and induced anisotropy, cyclic loading and small strain response. In this work, the numerical implementation of a bounding surface model for structured soils formulated by Kawadas and Belokas[l] in the explicit finite difference code FLAC is described. This model incorporates capabilities to simulate soil destructuring, inherent and induced anisotropy, cyclic loading and small strain response.
Figure: Bounding surface and yield "bubble" surface with conjugate and image stress points (left), and Ko compression stress path and bounding and bubble surfaces evolution with 2 unloading-reloading loops (right)
REFERENCES 1. Kawadas M, Belokas G. An anisotropic elastoplastic constitutive model for natural soils, in Desai et al. eds. Computer Methods and Advances in Geomechanics, Balkema, Rotterdam, 2001.
— 293 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Numerical Modeling of Consolidation of Marine Clay under Vacuum Preloading Incorporating Prefabricated Vertical Drains Sao Man Ho *, Thomas Man Hoi Lok Department of Civil and Environmental Engineering, University of Macau, Macau SAR, China Email: [email protected] Abstract This study is to investigate by numerical modeling the consolidation of marine clay at Macao under vacuum preloading. A two dimensional finite element program CRISP was used for the numerical modeling of consolidation of marine clay under vacuum preloading. A unit cylinder model with three soil layers, sand, marine and alluvium, with thickness 6m, 13m and 11m, respectively, was first established to examine the one-dimensional consolidation behavior of soils under vacuum preloading. Vacuum pressure generated nearly identical effects compared to a conventional surcharge pressure of the same magnitude under one-dimensional condition, as evidenced by the responses of the settlement. The major difference between surcharge and vacuum preloading was the pore water pressure change. When vacuum pressure was applied to soil, negative pore water pressure was generated. The pore water pressure reduced from its initial hydrostatic state by the amount of the vacuum pressure applied, whereas in the case of surcharge with the excess pore water pressure first built up from its initial hydrostatic state by the same amount as the surcharge and then gradually dissipated. Based on the results obtained from unit cylinder model, a two-dimensional model was constructed for a case study of vacuum preloading at Macao. Vacuum pressure of 80kPa was applied at the top of the soil layer, with negative pore pressure generated along the soil surface and the length of the vertical drains, which was different from past studies by simply fixing the negative pore pressure along the top boundary only (e.g., Park et al. 1997). Slurry wall with 8m of depth and 0.7 m of diameter, used to prevent vacuum loss around the treatment area, was also included to the soil model. In order to model the unlimited soil boundary in real situation, 30m of soil around the treated area was found to be sufficient. The lateral displacement at the border of the treated area was also investigated. It was noted that the direction of the lateral displacement was inward under vacuum preloading instead of outward in the case of surcharge preloading. The degree of consolidation was used as the main criteria for assessing the effectiveness of soil improvement. Factors affecting the degree of consolidation measurements based on settlement and pore water pressure were also discussed. REFERENCES 1. SAGE Engineering Ltd. SAGE CRISP: User Manual SAGE Engineering Ltd., 1999. 2. Park CL, Jeong HJ, Park JB, Lee SW, Kim YS, Kim SJ. A case study of vacuum preloading with vertical drains, in Davies MCR ed. Ground Improvement Geosystems: Densification and Rein forcement, Thomas Telford, London, UK, 1997, pp. 69-74.
— 290 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Numerical Simulation of Nonlinear Interaction of Soil, Superstructure and Thick Raft with Irregular Plan Yongfeng Du *, Shengkui Di, Hui Li, Yu Song, Xinghai Dang Institute of Earthquake Protection and Disaster Mitigation, Lanzhou University of Technology, Lanzhou, 730050 China Email: [email protected] Abstract Of all types of foundation for tall buildings, thick raft is used most frequently nowadays in China. With the rapid progress of economy, tall buildings with various shapes have been constructed in recent years, thus promoted the developing of thick rafts with irregular plans. This paper presents a finite element method (FEM) based analysis for the interaction of soil, tall building superstructure, and raft foundation with a irregular plan. The irregular boundary is simulated as four nodes isoparametric element, Mindlin model for moderate thickness in which transverse shear is considered is used in order to improve the accuracy of calculation. The ground stiffness matrix is calculated by Boussinesq model and the nonlinear analysis is proposed to consider the foundation detach from soil. It is found from the investigation that the calculation accuracy of elastic half-space ground model can be improved by adopting the load test results and this make the results of calculation close to the experimental value. A finite element method program IRF is worked out to calculate the interaction of raft foundation and soil using FORTRAN90. The program SUPER is worked out using substructure can be used for calculating reduced superstructure stiffness matrix and reduced load vector. Four different types of irregular foundations are used as numerical examples, and the results of distribution of settlement and principle stresses of the foundation are briefly illustrated.
— 294 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Numerical Simulations of the Behavior of Foundations on Reinforced Soil C.M.Tou,T. M. H. Lok* Department of Civil and Environmental Engineering, University of Macau, Macau SAR, China Email: [email protected], [email protected] Abstract Since after the discovery of the improvement of the ultimate bearing capacity of foundations with geosynthetics such as geotextiles, geogrid, etc., a lot of experimental studies have been carried out to investigate the optimium configurations of the geosynthetics. In this study, finite element plain strain numerical model was created to investigate several parameters that would probably affect the behavior of reinforced foundations. The model used Duncan Hyperbolic model to simulate the foundation soil. Failure was defined when the settlement of the foundation reached S= 0.30B. The parametric studies of the single-layer soil system include the depth to the first reinforcement layer, the length of the reinforcement, the number of reinforcement layers, spacing between the reinforcement, tensile strength of the reinforcement and types of soils such as cohesive and cohesionless soil. Based on the numerial simulation, it is shown that the optimum depth to the first reinforcement layer is at about 0.15B and the result implies that the reinforcement does not need to be anchored in any way prior to placing the fill, as was previously thought essential to achieve a completely reinforced soil system. Also, the increase in bearing capacity in cohesionless soil is much higher than in cohesive soil due to the different mechanisms of interaction between the reinforcement and the soil.
Figure: A FE plain strain model with reinforcement for single-layer soil system & optimum depth to the first reinforcement layer REFERENCES 1. Kotake N, Tatsuoka F, Tanaka T, Siddiquee MSA, Huang CC. FEM simulation of bearing capacity of level reinforced sand ground subjected to footing laod. Geosynthetics International, 8(6): 501-549. 2. Shin EC, Das BM. Experimental study of bearing capacity of a strip foundation on geogrid-reinforced sand. Geosynthetics International, 7(1): 59-71. — 297 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X.Aug. 21-23, 2006, Sanyo, Hainan, China ©2006 Tsinghua University Press & Springer
Optimization of Observation Condition on Inverse Analysis for Identifying Corrosion of Steel in Concrete Kazuhiro Suga l*9 M. Ridha2, Shigeru Aoki 3 1
Center for Computational Mechanics Research, Toyo University, Hakusan2-36-5, Bunkyo-ku, Tokyo 112-8611, Japan 2 Department of Mechanical Engineering, Syiah Kuala University, BandaAceh, Indonesia 3 Department ofComputational Science andEngineering, Toyo University, Toyo University, Japan Email: [email protected], [email protected], [email protected] Abstract The purpose of this study is to optimize the observation condition on the inverse problem for estimating the real and imaginary parts of the concrete conductivity and the impedance of the steel-concrete interface. The optimization is achieved by minimizing the average of eigen values of a posteriori estimate error covariance matrix. We performed a numerical identification to demonstrate the effectiveness of the optimized observation condition. The estimation is carried out by using the Kalman Filter algorithm. The simulation result shows that the real part of the impedance can be estimated with a high accuracy while the others cannot be well estimated. To overcome the above difficulty, a priori information and other kinds of observation conditions are considered. REFERENCES 1. Ridha M, Amaya K, Aoki S. Improvement of AC impedance method for monitoring corrosion of rebar structure by boundary element inverse analusis. Zairyo-to-Kankyo, 1999; 48: 654-659. 2. Amaya K, Aoki S. Optimization of measurements for inverse problem. Proc. 3rd Int. Conf. on Inverse Problems in Analysis, Port Ludlow, WA, USA, June 13-18,1999, pp. 1-6.
— 285 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Soil Additionally Affected by Non Force Loading and Its Influence on Upper Structure P. Kuklik *, M. Broucek Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thdkurova 7, 166 29 Prague 6, Czech Republic Email: [email protected] [email protected]; [email protected] Abstract It is an experimentally confirmed fact that a soil substantially changes its material properties when subjected to external loading. Apart from that, the soil, when subjected to a certain loading history, has the ability to memorize the highest level of loading mathematically represented by over-consolidation ratio, and so called initial void ratio. In virgin state the soil deformability is relatively high. On the contrary, following the unloading/reloading path shows almost negligible deformation until the highest stress state the soil has experienced ever before is reached [1,2]. The paper presents basic resources for the evaluation of the numerical codes for soils affected by floods. One of them is research project FLAMIS describing the 2002 year flood in the region of the South Bohemia. All substantial influences, such as suction, piping etc., can change the overconsolidation and porosity inside the subsoil. This affects the upper structure due to collapses of the soil skeleton following by the stress redistribution. Time dependent progress of influence zone can be used for the fast estimation of this phenomenon in the subsoil [3]. Several numerical examples are carried out using professional code GEO 5 FEM from FINE Inc. Ltd. The results are compared with real damages in situ.
REFERENCES 1. Bowles JE. Foundation analysis and design. McGraw-Hill, New York, 1966. 2. Kuklik P, Sejnoha M, Mares J. The structural strength of soil from the isotropic consolidation point of view. APCOM 99, Singapore, 1999, pp. 797-802. 3. Kuklik P et al. Calculation and verification of the influence zone depth inside the subsoil. ICCM 2004, Singapore, 2004.
— 295 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Stress-Based Effective Space Anisotropic Damage Model for Concrete Jian-YingWu^JieLi2 1
Department of Civil Engineering, South China University of Technology, Guangzhou, 510640 China Department of Build Engineering, Tongji University, Shanghai, 200092 China Email: [email protected]
2
Abstract Damage induced anisotropy is crucial for those initially isotropic materials, e.g., quasi-brittle materials such as concrete, geomaterials, ceramics, etc. Just as already pointed out by other researcher, at least second-order tensor should be adopted as damage variable to describe the damage induced anisotropy. Despite the substantial research efforts and the noteworthy recent contributions, the modeling of anisotropic damage is not a straight-forward task as that of isotropic one and still remains a challenging issue, among which the key point is the establishment of thermodynamically consistent damage evolution law. In this paper a stress-based effective space anisotropic damage model is proposed and applied to concrete modeling. The general stress-based formulations of modeling anisotropic damage with a second-order tensorial damage variable are first discussed, and then the principle of damage dissipation equivalence is introduced to define the effective damage rate tensor by transforming the nominal damage rate tensor. Therefore obtained by the corresponding inverse transformation, the conjugated effective damage energy release rate is completely and simply expressed in the effective space and exhibits some convenient properties. The damage criteria can thus be thermodynamically consistently postulated in terms of the obtained effective damage energy release rates, after which the damage evolution law in the effective space is then established in accordance with the principal of maximum damage dissipation. By incorporating the positive and negative projection operators, the presented framework is generalized to take the unilateral effect into account. The proposed model is applied to concrete modeling, leading to an anisotropic damage model which is capable of describingmost of the nonlinear anisotropic behavior of concrete evident in the experiments. It has been demonstrated that, only six material properties are required in the presented orthotropic damage model, i.e. the Young's modulus £ 0 , the Poisson's ratio vo, the uniaxial tensile and compressive strength f and^c, and the Mode-I and Mode-II fracture energy G\ and Gf , to describe most of the nonlinear behavior evident in the experiments, such as the stiffness degradation, the strength softening, the enhancement of strength and ductility under compressive confinement, the strength decay induced by orthogonal tensile cracking, the unilateral effect under cyclic loading and the damage induced anisotropy, etc. Most importantly, all the parameters are physically meaningful and can be easily identified by conventional experiment procedures, which constitutes the main merit of the presented model over others existing in the literature.
REFERENCES 1. Cordebois JP, Sidoroff F. Damage-induced elastic anisotropy. in Jean-Paul Boehler ed. Mechanics of Behavior of Anisotropic Solids, No. 295, Martinus Nijhoff Publisher, 1979, pp. 19-22. 2. Carol I, Rizzi E, Willam K. On the formulation of anisotropic elastic degradation. I: theory based on a pseudo-logarithmic damage tensor rate; II: generalized pseudo-Rankine model for tensile damage. International Journal of Solids and Structures, 2001; 38(4): 491-546. 3. Ortiz M. A constitutive theory for inelastic behaviour of concrete. Mechanics of Materials, 1985; 4: 67-93. — 287 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Stress-Strain Modeling of Tire Chip-Sand Mixture H. J. Yu**, Thomas M. H. Lok 2 1
Faculty of Science and Technology, University of Macau, Macao SAR, China University of Macau, Av. Padre Tomds Pereira S.J., Taipa, Macao SAR, China Email: [email protected], [email protected] Abstract The mechanical behavior of scrap tire chip-sand mixture was previously examined in laboratory for the use of scrap tire as a potential lightweight fill material. The purpose of this study is to numerically model the stress-strain relationship and volumetric behavior of tire chip-sand mixture with varying chip/mix ratio, by using two different modeling methods. One is the hyperbolic model, the other one is the artificial neural networks (ANNs). A series of triaxial consolidated-undrained (CU) and consolidated-drained (CD) compression tests for the tire chip-sand mixture of six different chip/mix ratio is performed under controlled conditions to develop the database. The test results were used for the hyperbolic modeling parameters determination and neural network training and testing. Comparisons between the laboratory testing results and the numerical modeling results indicate that the simple hyperbolic model has certain limitations in modeling the behavior of tire chip-sand mixture such as dilation and strain softening. On the other hand, ANN is a powerful mathematical tool for non-linear multi-variable analysis. As shown in the figure, the ANN based models have great capacity to simulate the effects of chip/mix ratio (R) on the stress-strain relations and volumetric behavior of the mixture. Details on training and learning algorithms to develop the models are discussed.
0
5
10
15
£
a(%)
20
0
5
10
15
£
a(%) 20
Figure: ANN simulation of stress-strain relationship and volumetric behavior during CD triaxial testing REFERENCES 1. Duncan JM, Byrne P, Wong KS, Mabry P. Strength, stress-strain and bulk modulus parameters for finite element analyses of stresses and movements in soil masses. Report No. UCB/GT/80-01, UCB, 1980. 2. Ellis GW, Yao C, Zhao R, Penumadu D. Stress-strain modeling of sands using artificial neural networks. Journal of the Geotechnical Engineering Division, ASCE, 1995; 121(5): 429-435.
— 298 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Stresses and Cracking Caused by Hydration Heat in Massive Concrete Structures Ziming Zhang1*, Zhitong Song1, Yan Zhang2 1
Department of Engineering Mechanics, Hohai University, Nanjing, 210098 China Department of Material Science, Hohai University, Hanjing, 210098 China Email: [email protected] 2
Abstract After development of the theory and analysis of the temperature [1], this paper analyzes the stresses and cracking caused by hydration heat in massive concrete wall. The analysis takes into account the fact that the adiabatic temperature rise and the creep model are based on Arrhenius' theory which lead to nonlinear differential equations, and the cracks are modeled by Bazant's crack band model [2]. The crack is divided into equal strips, and a numerical algorithm with step-by-step loading is developed to calculate the growth of the crack in each step. The interactions of temperature, stresses and cracking are computed by half-analytical iteration method. The systems of up to 360 nonlinear equations are solved in this paper. The following conclusions are drawn. A temperature increase has two mutually competing effects. Firstly, it accelerates creep, i.e. increase the creep rate. This indicates that the retardation or relaxation times should be reduced as temperature increases. Secondly, a temperature increase further causes an acceleration of hydration or aging, thereby indirectly also reducing creep. The placement temperature has a severe effect on cracking in massive concrete wall, the more the placement temperature, the earlier the crack happen, and the longer the crack length. REFERENCES 1. Bazant ZP, Oh BH. Crack Band Model Theory for Tracture of Concrete. Materials and Structures (RILEM. Paris), 1983; 16: 155-177. 2. RILEM Committee TC-69 (Bazant ZP et al.). Material Models for Structural Creep Analysis, Chapter 2. in Bazant ZP ed. Mathematical Modeling of Creep and Shrinkage of Concrete. John Wiley, Chichester and New York, 1988, pp, 99-200. 3. Bazant ZP, Cedolin L. Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories. Oxford University Press, New York, 1991.
— 289 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
A Continuous Approach to Discrete Structural Optimization T. Tan*, X.S.Li State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024 China Email: [email protected], [email protected] Abstract The mathematical model of the discrete optimization is generally defined as (PI): min f(x) s. t. gj(x)<0, j = \, 2,..., m xt £ S, = [sn, ..., siRj}, i = 1, 2,..., n where x is the design vector, S. stands for a specified discrete-valued set for x.. In this paper we introduce a continuous approach to solving discrete optimization problem (PI), which is both mathematically rigorous and easily implemented in engineering practice. With this approach, the variable x. is denoted by xi — ^2sirSir, and (PI) is converted into an equivalent 0-1 model (P2): r=\
min f(6) s.t. gj(6)<0,
y = l, 2,..., m
X X = 1, i = 1, 2,..., n\ 8ir e {0, 1}, i = 1, 2,..., *, r = 1, 2,..., R. r=\
It is interesting to note that this reformulation for (/?,) coincides with the segmental model [1]. However, a very different solution strategy is proposed with our continuous algorithm in which the constraint 6ir €{0, l } , is replaced by a continuous one -Sir\og6ir — (l — 5f>)log(l — ^.r) = 0 by means of so-called binary entropy function [2]. As such, we finally establish an equivalent continuous model (P3): min f(6) s.t. gj{6)<09 7 = 1,2,..., in X X = U
= 1,2,...,H;
r=\
-8ir\og6ir-{\-6ir)log{\-6ir)
= 0, i = l, 2,...,«, r = l, 2,...,/?,.
Numerical experiments give promising results for proposed algorithm. REFERENCES 1. Templeman AB, Yates DF. A segmental method for the discrete optimum design of structures. Eng. Opt., 1983; 6: 145-155. 2. Shannon CE. A mathematical theory of communication. Bell System Tech. J., 1948; 27: 379-423, 623-656. — 304 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanyo, Hainan, China ©2006 Tsinghua University Press & Springer
Application and Research of Structure Topology Optimization of Scraper Conveyer with MSC.Nastran.optishape J. B. Sang*, B. Liu, S. F. Xing, L. C.Yang, Y. H. Qie Department of Mechanical Engineering, Hebei University of Technology, Tianjin, 300130 China Email: [email protected] Abstract Within the last 30 years, a number of methods have been proposed such as boundary-based shape optimization, homogenization-based method, evolutionary structural optimization etc [1]. Design optimization is used to produce a design that possesses some optimal character, such as minimum weight. However, these optimization capabilities are basically used to improve the design of structures or parts in the detailed design process. In the beginning of conceptual design process, another method of optimization what is called topology optimization is necessary. Based on the homogenization method, which is introduced by Bendsoe and Kikuchi [2] in 1998, topology optimization has become an important and well-recognized sub-area of structure optimization. This theory has been extended and applied to several of kinds of problems such as static problems and mode problems [3]. In this paper, topology optimization of scraper conveyer is based on homogenization method and carried out with MSC.Nastran.optishape program. On the basis of this theory of homogenization method, the design domain is assumed composing of infinitely periodic microstructures [4]. Starting with a discussion on several of optimization methods and their merit and shortage, homogenization method is discussed completely [5]. In the first phase of topology optimization, the model of scraper conveyer is analyzed with MSC.Nastran. The results shows that the maximal stress value in original design is much less than the yield stress value, which make material wasted. Then the model is submitted to MSC.Nastran.optishape to access the topology optimization results. We find that the maximal stress value in scraper conveyer doesn't still approaches its breaking point. Therefore this design makes material sufficient used, the weigh of scraper conveyer effectively lightened and the stress distribution is more reasonable. It is found that optimization result is according to the theory and it is also testified that topology optimization with MSC.Nastran.optishape can be applied in the engineering scope practically. REFERENCES 1. Boltyanski V. Application of topology in optimization theory. Topology and Its Application, 2005; 617-628. 2. Bendsoe MP, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Comp. Meth. in App. Mesh. & Eng., 1988; 71: 197-224. 3. Bruns TE, Tortorelli DA. Topology optimization of nonlinear elastic structures and complaint mechaniasm. Computer Method in Applied Mechanics and Engineering, 2001; 3343-3359. 4. Fernandes P, Guedes JM, Rodrigues H. Topology optimization of three-dimensional linear elastic structure with a constraint on perimeter. Computers & Structures, 1999; 583-594. 5. Suzuki K, Kikuchi N. A homogenization method for shape and topology optimization. Comp. Meth. in Appl. Mech. & Eng, 1991; 93: 291-318. — 309 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Engineering Structural Optimization with an Improved Ant Colony Algorithm Y.B. Gong*, Q.Y.Li Department of Electronic Machinery and Traffic Engineering, Guilin University of Electronic Technology, Guilin, 541004 China Email: [email protected], [email protected] Abstract Ant colony optimization (ACO) algorithm is a newly developed bionics method, which has been successfully applied to several kinds of optimization problems as the traveling salesman problem, sequential ordering, and management of communications networks and so on. In this paper the ACO algorithms for optimization problems of engineering structure as the antenna structure was presented. It was shown how to construct the responding relations between the ACO algorithms and structural optimization problems. For improving the performance of ACO algorithms, several parameters of the algorithm, particularly the pheromone evaluation, had been improved here. Three examples on structural optimization were presented and solved by the improved ACO algorithms, Genetic Algorithm, Simulated Annealing Algorithm and so on. The comparisons between the improved ACO algorithm and other algorithm for the three examples have been obtained in terms of efficiency and effectiveness. The comparisons show the improved ACO algorithm is a very effective approach for solving structural optimization problems. And the improved ACO algorithm can greatly enforce the robustness of the optimal result. REFERENCES 1. Dorigo M. Optimization, learning and natural algorithms. PhD. Thesis, Politecnico di Milano, Italy, 1992. 2. Li QY, Li WY. Parallel genetic optimization design of antenna structure with simulated annealing mechanism, in Cheng GD, Olhoff N,Gu YX, Haftka RT eds. Structural and Multidisciplinary optimization, Proc. 4th World Congress WCSM04, Dalian, China, 2001: 241-242. 3. Gong YB, Li QY, Xiao ZX. The Application of ant algorithm in structural optimization, in Herskovits J, Mazorche S, Canelas A eds. Structural and Multidisciplinary optimization, Proc. 6th World Congress WCSM06, Rio de Janeiro, Brazil, 2005, No.4101.
— 301 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Evolutionary Topological Design of Frame for Impact Loads Xianyan Chen ! *, Qing Li *'2, Shuyao Long ! , Xujing Yang3 1
Department of Engineering Mechanics, Hunan University, Changsha, Hunan, 410082 China School of Engineering, James Cook University, Townsville, QLD 4811, Australia Key Laboratory of Advanced Technology for Vehicle Body Design & Manufacture of Ministry of Education, Hunan University, Changsha, 410082 China Email: [email protected]; [email protected]; [email protected] 2
Abstract Over the past decade remarkable progress has been made in the development of software used in crash simulation and analysis. A number of commercial codes have been available with accepted accuracy. However, there has been limited report in its inverse problem yet, i.e. topological and shape optimization for crashworthiness. The difficulty is primarily raised from two folders on (1) the nonlinear sensitivity analysis and computational cost, which become particularly challenging in various topological designs; (2) dynamic multi-modals and non-convex design space, which do not lend the crash problems themselves well to classical gradient techniques. This paper aims at developing an alternative approach to the crashworthiness design problems. The Evolutionary Structural Optimization (ESO) will be applied to reduce the dependence on the continuum sensitivities. In a crash simulation, it is frequently found that plastic deformation in some locations may be much higher than others. This implies that the material of the crashing elements may have different contributions to the crashworthiness goal. Ideally, the energy absorption levels in all location are near identical. To represent the relative performance of element's material, a dimensionless factor is formulated by dividing the crash energy absorption by each element to the highest one as, a* =U.IU ^
11
max
where Ut computes the strain energy absorbed by the candidate element (zth). It is worth pointing out that the total internal energy should contain the elastic and plastic components, i.e. U = Ue+Up. The factor a1 can be used to determine the relative efficiency of material usage. By gradually removing the inefficient material of the elements from the structure, the remaining structure evolves toward an optimum. The non-linear explicit finite element code LS-DYNA is employed to simulate the deformation and stain energy of the structure under impact load. The ESO method is implemented in an environment of LS-DYNA. An example of frame topology designs are also shown in this study to demonstrate the capabilities of the present method.
REFERENCES 1. Pedersen CBW. Topology optimization design of crushed 2D-frames for desired energy absorption history. Structural and Multidisciplinary Optimization, 2003; 25: 368-382. 2. Steven GP, Li Q, Xie YM. Evolutionary topology and shape design for general physical field problems. Computational Mechanics, 2000; 26: 129-139.
— 307 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Multi-Objective Optimization for Shape Design of Arch Dams Linsong Sun1*, Weihua Zhang1, Nenggang Xie2 1
College of Hydraulic Science & Engineering, Yangzhou University, Yangzhou, 225009 China College of Mechanical Engineering, Anhui University of Technology, Maanshan, 243002 China Email: [email protected] 2
Abstract A multi-objective optimization model is established for the shape design of arch dams. In this model, the geometric parameters describing dam shape is taken as design variables; four objectives are considered of dam volume, maximal tensile stress, maximal pressure stress and relative depth of the zone with tensile stress that is larger than l.OMPa; and the constraints include geometric constraints, dam volume constraint and mechanical property constrains, i.e., stress constraints, stability constraints, etc. Traditionally, multi-objective optimization schemes transform multiple objective functions into a single objective function in some manner, weighted sum method and Utopia point method for examples, and the resulting problem is solved as a single objective optimization problem. In this paper the cooperative game model analogy to the multi-objective optimization is proposed with each player correspond to one of the objective functions. After defining the utility of each player, the Nash arbitrary scheme is used to solve the cooperative game. The optimization of Baihetan arch dam, which is located in Sichuan province of China, is calculated as an engineering example. The results are compared to those obtained by weighted sum method and Utopia point method and indicate that the cooperative game method is superior to traditional methods. The optimal design saves 9.77x104m3 of dam volume, compared to initial design, along with the decrease of maximal tensile stress with 38.22%, the decrease of maximal pressure stress with 28.83%, and the decrease of relative depth of large tensile stress zone with 10.15%. REFERENCES 1. Marlers RT, Arora, JS. Survey of multi-objective optimization methods for engineering. Struct. Multidisc Optim, 2004; 25: 369-395. 2. Sun Wenjun, Sun Linsong, Wang Dexin, Li Chunguang. Bin-objective shape optimization of arch dams. Journal of Hohai University (Natural Sciences Edition), 2000; 28(3): 39-43 (in Chinese). 3. Spallino R, Rizzo S. Multi-objective discrete optimization of laminated structures. Mechanics Research Communications, 2002; 29:17-25.
— 299 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Optimal Shape Control of Multilayered Piezoelectric Smart Plate Structure Jianguo Wang *, Genfang Ding, Yan Qin School of Civil Engineering, Hefei University of Technology, Hefei, 230009 China Email: [email protected] Abstract The finite element equations are derived by application of the extended Hamilton principle based on the classic electroelastic theory. Mechanical-electric coupled program has been developed by use of ANSYS/APDL language. A sandwich plate with embedded piezo actuators and/or surface bonded piezo actuators are modeled. The piezoelectric patch size and voltage are considered as design parameters. Zero order and first order optimal algorithms are also applied in order to maximize the piezoelectric actuator efficiency, improve the structural performance. To show the performance of the proposed models, several simple examples are presented. Results show that the presented model is effective. The some conclusions are presented in optimal design and shape control for smart structures.
50x10*
-1.0x100
100
Figure 1: Desired target shape of plate
0
Figure 2: Actual shape of plate after optimization
REFERENCES 1. Crawley EF, Deluis J. Use of piezoelectric actuators as elements of intelligent structures. AIAA J, 1987; 25(10): 1373-1385. 2. Adali SJ, Bruch JC, Sadek IS et al. Robust shape control of beams with load uncertanties by optimally placed piezo actuators. Structural and Multidisciplinary Optimization, 2000; 19: 274-281. 3. Barboni R, Mannini A, Fantini E et al. Optimal placement of PZT actuators for the control of beam dynamics. Smart Materials and Structures, 2000; 9: 110-120.
— 300 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Optimization Studies for Crashworthiness Design using Response Surface Method Xingtao Liao1*, Qing L i 1 2 , Weigang Zhang1 1
State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, 410082 China 2 School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW 2006, Australia Email: [email protected], [email protected] Abstract Structural optimization related to crashworthiness and impact energy absorption capability is of particular importance to the automotive industry, which involves highly nonlinear computational analysis and design with many material and structure parameters. Unfortunately, conventional design analysis techniques can only improve the structural crashworthiness to a limited extent, which frequently undergo significant difficulties to achieve a global optimized performance in a nonlinear analysis and design framework. This paper developed an innovative Response Surface Method (RSM) to tackle the crashworthiness design problems, where the number of FE analyses are significantly reduced. Objective and constraint functions in crashworthiness design problems are often non-smooth and highly nonlinear in terms of design variables and require considerably expensive computational effort. In this study, the approximations of objective and constraints with respect to the specific design variables are constructed by using a statistical modeling technique for the response surface method. These statistical approximations, or metamodels, are used to improve high cost simulations for facilitating crashworthiness optimization. This paper presents two novel examples with a certain practical implication, one thin plate with a square hole and one simplified front rail structure of vehicle. Both models were subjected to an impact into a rigid wall and the simulations were carried out in LSDYNA. The first problem aims to maximize the energy absorbed with the position and the shape of the hole as variables. The second problem focuses on minimizing the mass of the front rail structure meanwhile meet the requirement of crashworthiness performance using the gage thickness and the material properties as variables. In the latter, variable screening technique and the sequential approximate optimization method are used to improve the performance of Response Surface Method, which has more design variables than in the former and thus appreas more challenging in computational analysis and optimization. The results demonstrate that the new computational design method is efficient and effective in solving crashworthiness design optimization problems. REFERENCES 1. Stander N, Craig KJ. On the robustness of the successive response surface method for simulationbased optimization. Engineering Computations, 2002; 16: 431-450.
— 302 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Optimum Design of Spiral Grooved Mechanical Seal Based on Thermo-Hydrodynamics J. F.Zhou*,B. Q. Gu College of Mechanical and Power Engineering, Nanjing University of Technology, Nanjing, 210009 China Email: [email protected], [email protected] Abstract The spiral grooved mechanical seal is a new type of non-contacting mechanical seal, and is widely used as shaft sealing on pumps, compressors and agitators. A finite element program is developed to calculate the bearing force and the leakage rate of the fluid film in the spiral grooved mechanical seal. Based on the frictional heat transfer analysis of the sealing members and the coupling analysis of their thermal deformation and the frictional heat of the fluid film, the shape of the gap between the two deformed end faces and the viscosity of the fluid film can be determined when the bearing force of the fluid film is given. The optimum design of the spiral grooved mechanical seal is desired to obtain the optimal configuration of the sealing members which is corresponding to both the largest ratio of the stiffness of the fluid film to the leakage rate and the minimum temperature of the sealing members. By means of this technique, the optimal geometrical parameters of the sealing members are obtained, such as the length L, the inner radius R[, the outer radius R0, the end radius of the grooves Rg, the spiral angle a, the ratio of the groove width to the weir width S and the number of the grooves JVg, and the sealing members designed possess good heat transfer performance and sealing capability. Dam
„T .
Rotation
Figure: Model of the optimal spiral grooved seal ring REFERENCES 1. Pascovici MD, Etison I. Thermo-hydrodynamic analysis of a mechanical face seal. Journal of Triboligy, 1992; 114: 639-645. 2. Gabriel, Ralph P. Fundamentals of spiral groove noncontacting face seals. Lubrication Engineering, 1994; 50(3): 215-224. 3. Cicone T, Pascovici MD, Tournerie B. Non-isothermal performance characteristics of fluid film mechanical face seals. Journal of Engineering Tribology, 2001; 215(1): 35-44. — 306 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Parametrical Analysis and Optimization of Partial Double-Layer Reticulated Shells Using Uniform Design Method and Second Order Rotation Method J. C. Xiao1*, T. Liang1, Y. Liu2 1
School of Civil Engineering & Architecture, Guizhou University, Guiyang, 550003 China Department of Civil Engineering, Dalhousie University, Halifax NS B3J1Z1, Canada Email: [email protected] Abstract Partial double-layer reticulated shells are of the capability to cover large span space. To fulfill the requirements of preliminary design of the structures, uniform design method and rotational second order method are adopted to make parametrical analysis and optimization. Compared with other response surface methods, this approach needs fewer experiment observation times for the same precision. In the analysis, just existing software packages for structural analysis and design are used. By means of regression of the calculation results, approximate functional relations between the objective values (steel weight, deflections, basic frequency and minimal geometrically nonlinear buckling load) and the design variables (rise of shell, single-layer area, and design stress ratio for single-layer members), and the significant order of factors, are obtained. In these functions, the interactions of design variables are considered. The optimum level combination of the factors that meet the requirements of design specifications is obtained by solving a simple programming problem. Design verification of a multipoint-supported hexagonal partial double-layer reticulated shell shows the reliability of the results, which precision is high enough for preliminary design.
REFERENCES 1. Chen WJ, He YL, Fu GY. Stability analysis of the partial double-layer forms derived from the complete double-layer reticulated dome. Journal of the International Association for Shell and Spatial Structures, 2001; 42 (12): 117-127. 2. Cochran WG, Cox GM. Experimetal Design (second edition), John Wiley & Sons Inc, New York, 1957. 3. Mbakogua FC, Pavlovic MN. The prestressing of shell roofs. Engineering Structures, 1999; 21: 16-33.
— 305 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X,Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Path Optimization of Large-Scale Automated Three-Dimensional Garage Based on Ant Colony Algorithm Jianjun Meng **, Zeqing Yang \ Zhenrui Peng 2 1
Institute of Mech-Electronic Technology, Lanzhou Jiaotong University, Lanzhou, 730070 China National Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, 310027 China Email: [email protected], [email protected] 2
Abstract The basic principle of the ant colony algorithm was introduced firstly, and mathematical model was established taking the TSP (Traveling Salesman Problem) as the example. In view of computational complexity, lower efficiency and stagnation of this model, the max-min ant colony algorithm (MMACA) was proposed. Only the best ant that constructed the shortest tour is allowed to deposit the pheromone utilizing the historical information, which can effectively avoid the pheromone of one way is bigger than other ways leading to all ants concentrate to the identical way. But when it is applied in the actual scene of big disturbance, the search ability is unsatisfactory. To settle the contradiction among convergence speed and precocity and stagnation in the other ACAs, a new-type intellectual ant colony algorithm (NIACA) was developed. The proposed intellectual ACA adopts a novel dynamic pheromone updating rule to guarantee the algorithm has the better convergence speed and the stability; it uses a particular variation scheme in genetics to optimize each searched result, a new individual is produced using single-parent exchange operator and inversion operator and is applied to by inverse variation method to change the variation conditions. The performance of iteration will be improved and the time will be greatly reduced owing to this mutation operation. Meanwhile it introduces artificial interference to adjust the chosen path dynamically and consider the energy consumption. NIACA is applied to the path optimization of the large-scale automated three-dimensional garage. We have carried on the test on Personal Computer (PC) with the higher-level language, the results show that the improved algorithm has higher convergence speed and stability, and it can get ideal searching result. The time for taking and parking vehicles in garage is greatly reduced and the efficiency is greatly improved. Meanwhile, this algorithm has good robustness and can be carried out in parallel mode. Moreover, we also have experimented with the artificial interference to this algorithm, the simulation results indicate that the strategy leads to the dynamic adjustment of the selected path, and the feasible path that blocks the entrance task will be discarded and the optimized path with fewer energy consuming will be saved. It can reduce the computational complexity greatly, and it can get ideal searching results in the fewer iterations. The research results show that the prospect of this algorithm in large-scale optimization problems is promising. REFERENCES 1. M. Dorigo, V. Maniezzo, A. Colorni.The Ant System: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics, Part-B, 1996; 26: 1-13. 2. M. Dorigo, G. Di.Caro, L. M. Gambardella. Ant algorithms for discrete optimization. Artificial Life, 1999; 5: 137-172. 3. M. Dorigo, L. M. Gambardella.Ant colonies for the traveling salesman problem. BioSystems, 1997; 43: 73-81. — 303 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Structural Topology Optimization Using Level Set Method Michael Yu Wang * Department of Automation & Computer-Aided Engineering, The Chinese University of Hong Kong, Shatin, NT, Hong Kong, China Email: [email protected] Abstract Structural optimization, in particular the shape and topology optimization, plays an important role in structural design and analysis. Optimization techniques could deliver a design with optimal performance requirements such as strength, stiffness, weight, natural frequency, or buckling. Particularly, topology optimization has the greatest potential for the improvement in structural performance, since topology optimization procedures permit changes in the connectivity of the geometry of the structure during the design process. Over the past decade, there have been some extensive developments of various approaches to topology optimization. Here, we specifically put forth the level set method, in which the shape of a structure is employed and modified directly such that certain design objectives are obtained. The level-set method is a versatile and efficient technique for problems involving the motion of curves and surfaces. It is by now a classical tool in many fields of applications such as fluid mechanics and image processing. For structural topology optimization, the technique makes use of the classical shape sensitivity in an Eulerian framework. One attractive attribute of the method is that it gives a natural way of describing closed boundaries (curves or surfaces) and allows for automatic changes of topology, such as merging and breaking of boundaries, with calculations easily made on a fixed rectilinear grid. Over the recent years, the technique has been developed for many topology optimization problems, including solid structures [1] materials [2], and compliant mechanisms [3]. A bridge type structure is presented in this paper to illustrate the technique. It can be concluded that the topology optimization using level-set method is a novel technique for structure optimization. It yields a complete solution space and allows for the application to complex engineering problems, including material, boundary and geometric behavior, linear or nonlinear. It is suitable for complex problems and has been successfully used in industry for engineering designs.
REFERENCES 1. Wang MY, Wang X, Guo D. A level set method for structural topology optimization. Computer Methods in Applied Mechanics and Engineering, 2003; 192(1): 227-246. 2. Wang MY, Zhou SW. Synthesis of shape and topology of multi-material structures with a phase-field method. Journal of Compute-Aided Materials Design, 2004; 11(2-3): 117-138. 3. Wang MY, Chen SK, Wang X, Mei Y. Design of multimaterial compliant mechanisms using level-set methods. Journal of Mechanical Design, Trans, of ASME, 2005; 127(5): 941-956.
— 310 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Topological Optimization Analysis of 3-D Continuum Structure with Stress and Displacement Constraints* H. L. Ye*, Y. K. Sui Numerical Simulation Center for Engineering, Beijing University of Technology, Beijing, 100022 China Email: [email protected], [email protected] Abstract It is well known that topology optimization of 3D continuum structure is one of the major challenges because of difficulty to establish a good geometric model which comprising a large number of design variables, and complexity of optimization algorithm. On the other hand, the problem under multiple load case is not easy to be approached than one under single load case, because the former becomes a multiple objective problem based on compliance objective function. In order to overcome these difficulties, the optimal topology model of 3D continuum structure is established based on ICM (Independent Continuous Mapping) method, which refers to weight as objective and subjected to stress constraints and displacement constraints with multi-load-cases. A globalization of stress constraints is proposed by virtue of the von Mises' yield criteria in theory of elastic failure. Thus, transformation of all elements' stress constraints into a structural energy constraint is achieved, namely, a global constraint substitutes for lots of local constraints. As a result, the numbers of constraints is reduced, and the complexity of the sensitivity analysis is decreased. For global displacement constraints, an explicit expression of displacement with respect to the topological variables is formulated by using of unit virtual load method. In order to decrease the error of numerical calculation generated by the order magnitude between different physical quantities, the optimal model that normalizes with two types of dimensionless constraints is further derived for continuum structure with stress constraints and displacement constraints. Furthermore, the best path transmitted force in the multiple load cases is selected successfully. The dual quadratic programming is applied for to solve the optimal model of continuum. Consequently, the number of design variables is dramatically decreased; the efficiency of computation is improved. In addition, the present optimal model and its algorithm have been implemented by means of the MSC/Patran software platform using PCL. Several numerical examples indicate that the method is effective and efficient. As an example, Figure 1 illustrates the background structure of an elastic body with size 10X0. 6X2m 3 . The two corner points on the bottom side are fixed. Four central forces P\ = P2 = P3 = PA = 450 kN are located in the middle of top of beam. The allowable stress is 50 Mpa, and the displacement constraint value of the four nodal points where the forces are located is less than 0.8 mm along with the up-to-down direction. The optimal topology configuration of the structures is illustrated in Figure 2.
Figure 1: Finite element model
Figure 2: Optimal topology configuration
* Supported by the National Natural Science Foundation of China (10472003), Beijing Natural Science Foundation (3002002), Beijing Educational Committee (KM200410005019) and the Foundation of Beijing University of Technology for PhD. — 311 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Topology Optimization of Space Vehicle Structures Considering Attitude Control Effort Z. Kang*, C. Zhang State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, 116024 China Email: [email protected] Abstract This paper addresses the topology optimization of space vehicle components for reducing the attitude control efforts. The driving torque requirements for attitude control of a space vehicle are typically closely related to the mass moment inertia of the system. Particularly, as shown by the present study, the air consumption for attitude control actuators using compressed cool air is proportional to the mass moment of inertia. In such circumstances, it is meaningful to reduce the mass moment of inertia of the structural components in order to minimize the attitude control efforts. While structural topology optimization problems are conventionally formulated as to minimize the structural weight (or material volume) or to optimize the structural performance (compliance, eigenfrequencies, etc.) under material volume constraint, the problem for minimum compliance under constraints of mass moment of inertia is investigated in this paper. The SIMP approach (Bendsoe M.P. 1989) is used in the mathematical statement of the problem, where the material density of the artificial material for each element is taken as the design variable. For the solution of the problem with a single constraint on the moment of inertia, the Optimality Criteria method is employed. To this end, a design variable updating scheme is derived based on the Kuhn-Tucker optimality condition. Therein, a sensitivity filtering technique proposed by O. Sigmund (1997) is employed to alleviate numerical instabilities such as checkerboard and mesh-dependency problems. For problems with multiple constraints, the gradient-based Mathematical Programming approach is employed. Numerical examples will be given for demonstration of the validity of the present method. The different optimal structural layouts obtained with the proposed formulation and those with the conventional topology optimization will be also discussed. REFERENCES 1. Bendsoe MP. Optimal shape design as a material distribution problem. Struct. Optim., 1989; 1: 193-202. 2. Sigmund O. On the design of compliant mechanisms using topology optimization. Mech. Struct. Mach., 1997; 25: 495-526.
— 308 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
A hybrid elasticity method for bending and free vibration of composite laminates C. F. Lu, W. Q. Chen* Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China Email: [email protected] Abstract Semi-analytical solutions for bending and free vibration of composite laminated beams and plates have been derived based on 2D/3D elasticity theory using a newly developed hybrid analysis, which perfectly combines the state space approach (SSA) and the differential quadrature (DQ) technique. The thickness direction of laminates is selected to be the transfer direction in SSA, and the DQ technique is employed to discretize the domain(s) normal to the transfer domain. This enables us to transfer the original partial differential equations into a state equation consisting of first-order ordinary differential equations. In particular, the use of DQ technique makes ease of the treatment of various boundary conditions, which can not be considered in the conventional exact state-space approach. A transfer relation between the state vectors at the top and bottom surfaces of the laminates using matrix theory is established, from which the bending and free vibration problems can be solved eventually. Comprehensive numerical results have been obtained, which converge rapidly and agree well with that in the literature as well as finite element calculations. It is concluded that: (1) the DQ technique significantly widens the application of SSA; and (2) the proposed method is very efficient for analyzing layered structures. REFERENCES 1. Bahar LY. A sate space approach to elasticity. Journal of the Franklin Institute, 1975; 299: 33-41. 2. Bellman R, Casti J. Differential quadrature and long-term integration. Journal of Mathematical Analysis and Applications, 1971; 34: 235-238. 3. Shu C, Richards BE. Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids, 1992; 15:791-798.
— 327 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
A New Multi-Harmonic Method for Predicting the Forced Response of Mistimed Bladed Disks with Dry Friction Damping* Erming He, Hongjian Wang * College ofAeronautics, Northwestern Poly technical University, XVan, 710072 China Email: [email protected], [email protected] Abstract Mistiming refers to the variations of blades properties due to procession and wear etc. Though these variations is small, they can confine the vibration energy in a few blades, and increase the resonant response of those blades. Therefore, dry friction dampers are often used to reduce the vibration of blades. In order to investigate the effects of mistuning and the performance of dry friction dampers, it is necessary to develop an efficient numerical method to predict the resonant features of the bladed disks with dry friction dampers. We propose an efficient multi-harmonic (MH) method which is based on the harmonic balance method. The formulation of the method can take the advantage of fast Fourier transformation (FFT) which can facilitate the analysis efficiency significantly. The iterative Newton-Raphson procedure are used to solve the nonlinear vibration equation. The MH method has been used in a mass-string model of bladed disk, and validated by numerical integration method. The analysis of forced response features is performed by the MH method for both tuned and mistuned systems with various coupling strength, viscous damping, dry friction damping and blade stiffness mistuning etc. The results indicate that the MH method can efficiently predict the resonant response of the bladed disks with nonlinear dry friction damping. It is found that, for the weakly coupled bladed disk with nonlinear blade-to-blade dry friction damping, mistuning can reduce resonant amplitudes of the system significantly when dry friction and viscous damping are all smaller. This is not common for mistuning effects. In other situation, Mistuning can increase the resonant amplitudes, broaden the resonant frequency region, and produce multiple resonant peaks. REFERENCES 1. Griffin JH, Sinha A. The interaction between mistuning and friction in the forced response of bladed disk assemblies. Journal of Engineering for Gas Turbines and Power, 1985; 107: 205-211. 2. Wei ST, Pierre C. Effects of dry friction damping on the occurrence of localized forced vibrations in nearly cyclic structures. Journal of Sound and Vibration, 1989; 129(3): 397-416. 3. Berthillier M, Dupont C et al. Blades forced response analysis with friction dampers. ASME Journal of Vibration and Acoustics, 1998; 120: 468-474. 4. Cardona A. A multiharmonic method for non-linear vibration analysis. International Journal for Numerical Methods in Engineering, 1994; 37: 1593-1608.
* This work is supported by the National Natural Science Foundation of China (No.50275121) — 324 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanyo, Hainan,China ©2006 Tsinghua University Press & Springer
A Web-Based Data Management and Decision Support System for Slope Safety Inspection and Evaluation J. Wang1*, M. C. Hung2 1
Department of Civil Engineering, Tamkang University, Tamsui, Taipei County, Taiwan, China MIS Division, Yosun Industrial Corp., Taipei, Taiwan, China Email: [email protected]
2
Abstract This paper examines how artificial intelligence and WWW technologies can be applied to disaster management to improve the current practice. A web-empowered database and decision support system was built for slope safety inspection and evaluation of residential communities on hillsides. Users can perform data management directly through the browser interface without any knowledge of database and query language. Furthermore, the system is capable of adding communities and instruments, as well as other text and image information of the communities on-line. As for safety evaluation, rule-based reasoning is used to decide the safety degree of every monitoring instrument. The system was implemented with the three-tier software architecture. The web-based environment let users use standard WWW browsers to enter, inquire and manage monitoring data without installing additional programs. The inference engine of the system is WebExpert [1] installed on a MS 2000 server with IIS. Its programming language is based on CLIPS [2], a lisp like and rule-based language. In addition, the system incorporates dynamic graph generation together with a friendly user interface implemented in HTML and JavaScript, etc. The system performs as an efficient tool for the safety inspection and evaluation of hillside residential communities. It acts as a collaboration portal that collects monitoring data, text and picture information from field safety inspectors at different locations. Also, it acts as an information and data visualization portal with various graph generation and decision support functions for government officials to evaluate the safety of the communities.
Jfi&£> Residents
JKk Government Officials
ODBC database*.
Internet or Intranet
DSS
Inspectors
Wi,i
,i mp.ffn,,,<M'»II m »mwv,f
iV^^fe-
HTTP
CGI
Server—
OS: Windlm 2000 Server IS:HS Inference Engine: WebExpert
Figure: Overview of the slope monitoring system REFERENCES 1. WebExpert Technical Reference Manual, Wise Web Ware, Inc., 2001. 2. Riley G. CLIPS: A Tool for Building Expert Systems, at http://www.ghg.net/clips/CLIPS.html, accessed February 2006. — 318 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Active Vibration Control Analysis of Piezoelectric Intelligent Beam Tao Wang, Rong Qin *, Guirong Li Department of Architecture and Civil Engineering, Guangxi University, Nanning, 530004 China Email: [email protected], [email protected], [email protected] Abstract The new theory and new method of the analysis of intelligent structures are studied in the paper. With piezoelectric intelligent beam as a example: the spline dispersing dynamical equations of the piezoelectric intelligent beam is given by the spline finite-point method, from the displacement modal, basing on intelligent constitutive relation theory, instantaneous variational principle and spline dispersing. Then the control equation of the active vibration control analysis of the piezoelectric intelligent beam is get. In the paper, considering the influence of transverse shear deformation in the geometric equations, using the intelligent linear elastic constitutive relation of piezoelectric materials and the end loop feedback control. Modeling process include: spline dispersing, establishing the intelligent spline dispersing functional, establishing the intelligent spline dispersing dynamic equations and establishing the active control equations of the intelligent beam. Two typical examples are studied: one is the electro-mechanical coupling analysis of piezoelectric bimorph beam and the other is the active vibration control analysis of the intelligent beam with a single piezoelectric patch. The results are well closed to the theoretical solution and the experimental result. Using spline finite-point method could make the physical conception be definitude and the logic clear. Simultaneity, could deal with the stiffness matrix, load matrix and electro-piezoelectric matrix easily. The results indicate that spline finite point-point method used in the paper, with simply calculation and high precision, is a powerful and economical method. REFERENCES 1. Tzou HS. Development of a light-weight robot end-effect using polymeric piezoelectric bimorph. Proceeding of the 1989 IEEE International Conference on Robotics and Automation, 1989, pp. 17041709. 2. Qin Rong. Intelligent Sttructure Mechanics. Science Press, Beijing, 2005 (in Chinese). 3. Wang Shuhe. Electric-piezoelectric Analysis and Active Vibration Control Research of Piezoelectric Laminated Plate/Shell Structures. PhD Thesis, Tianjin University, Tianjin, China, 1997 (in Chinese).
— 331 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Application of Translation Corresponding Tree (TCT) Annotation Schema for Chinese to Portuguese Machine Translation Chi-Wai Tang , Fai Wong, Ka-Seng Leong, Ming-Chui Dong, Yi-Ping Li Faculty of Science and Technology, University of Macau, Macau SAR, China Email: {kevin, derek, sejohnny, dmc}@inesc-macau.org.mo, [email protected] Abstract In Example Based Machine Translation (EBMT) research, there are three main approaches: Surface Based, Pattern Based and Structure Based approach. In Structure Based EBMT system, such as SSTC approach [1], it has a problem that it relies on two syntax parsers to analyze the translation examples, but robust syntax parsers are not always available. On the other hand, Chinese and Portuguese belong to two different language families and there exist grammatical deviation problem between them. In order to resolve the weakness of the Structure Based EBMT system and linguistic problems between Chinese and Portuguese, Tang and Wong [2] propose a new Portuguese to Chinese Machine Translation method and this method is based on a novel technology called Translation Corresponding Tree (TCT) which is an example based knowledge annotation method for Portuguese to Chinese translation. In this paper, it adopts the TCT annotation scheme and introduces the knowledge based construction and translation for Chinese to Portuguese MT. In this parper, it presents the additional problems during Chinese analysis and the corresponding solutions. In this research, it also proposes a conversion algorithm to reuse the existing translation knowledge of Portuguese to Chinese MT system, which represented in terms of TCT trees. Based on the transformation algorithm, the knowledge trees of Portuguese to Chinese translation is converted into that of the translation knowledge which can be used to facilitate the Chinese to Portuguese . By this conversion method, existing knowledge can be easily reused without having to re-construct the knowledge from scratch. Based on the research result of this paper, a Chinese to Portuguese prototyping machine translation system is implemented and the empirical results show that the MT system can achieve the translation accuracy of 85% in the domain of Macau Law statements. REFERENCES 1. AI-Adhaileh MH, Tang EK, Zaharin Y. A synchronization structure of SSTC and its applications in machine translation. The COLING 2002 Post-Conference Workshop on Machine Translation in Asia, 2002. 2. Tang CW, Wong F, Li YP. TCT Schema in EBMT and its application. In Proc. the Symposium on Applied Science and Technology in Macau 2004, 2004, pp. 19-27.
— 315 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Coupled Vibration Analysis of Multiple Launch Rocket System by Finite Element Method Bingshang Li, Xinqi Xu * Naval Aeronautical Engineering Institute, Yantai, Shandong, 264001 China Email: [email protected] Abstract In multiple launch rocket system, initial disturbing is one important factor to influence the firing precision. It is meaningful theoretically and valuable practically to Study and to take right theory and effective calculating methods to analyze the vibration of the multiple launch rocket system . Based on CSG (Constructive Solid Geometry) and FEM (Finite Element Method), the elastic multiple launch rocket system modal is built and the vibration-coupling response of multiple launch rocket system when firing constantly is simulated. In order to verify the availability of researching methods, the conclusions are compared to practical situation.The result provides scientific basis for multiple launch rocket system design. REFERENCES 1. Xiaoting Rui, Yuqi Lu. Simulation and Test Methods of Launch Dynamics of multiple launch rocket system. National Defense Industry Press, Beijing, China, 2003 (in Chinese). 2. Guoping Wang, Xiaoting Rui, Weidong Chen. Dispersion Simulation Technique of Multiple Tube Weapon. Journal of system simulation, 2004; 16 (5): 963-966 (in Chinese).
— 325 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Cross-Level Sentence Alignment Anna Ho *, Francisco Oliveira, Fai Wong Department of Computer Science, Faculty of Science and Technology of University of Macao, PO Box 3001 Macao SAR, China Email: [email protected] Abstract This paper describes a new model for sentence alignment system of structurally different languages such as Chinese and Portuguese. The alignment may be one-to-one, one-to-many, many-to-one and many-to-many. It is also not surprised that the first word or sentence of Chinese is a translation of the last word or sentence of Portuguese. In this proposed method, we try to combine the statistical approach and lexical approach in order to achieve the efficiency and accuracy. In our current research, we first complete the word level alignment by making use of the Chinese-Portuguese dictionary to get the basic translation rate between the two texts. However, the system cannot make a good decision in processing the word alignment by just only concerning the information achieved from the Chinese-Portuguese dictionary. This is because most often the named entities cannot be discovered from the dictionary and this causes the system make a wrong decision. In order to make the system more adaptive, we apply the maximum entropy model to align the named entities without perform the word segmentation for Chinese. Secondly, from the word level alignment, we achieve anchor point and process the sentence level alignment. We use the Hidden Markov Model (HMM) and Singular Value Decomposition (SVD) to get the statistical information of the sentences. For SVD model, we first set up a matrix which consists of the word level alignment statistic information. Then performs the two dimensional reconstruction of the original matrix. By comparing Figure 1 and Figure 2 (sample fragments of data), we can observe some relationships among the sentences and this can give an approximation of sentence alignment. Table: Original matrix (left) and 2D reconstruction of the original matrix (right) PI P2 P3 P4 P5 P6 P7 P8 P9 P10
CI 6 5 1 1 2 1 1 0 11 3
C2 2 4 0 1 1 1 0 0 7 3
C3 2 4 0 1 1 1 0 0 7 3
C4 6 4 1 1 2 1 1 0 12 3
C5 2 4 0 1 1 1 0 0 7 3
C6 2 4 0 1 1 1 0 0 7 3
C7 2 4 0 1 1 1 0 0 7 3
Pi P2 P3 P4 P5 P6 P7 P8 P9 P10
CI
C2
C3
C4
C5
C6
C7
5.74 4.51 0.92 1.02 1.94 1.02 0.92
2.09 3.92 0.04 0.98 1.01 0.98 0.04
2.09 3.92 0.04 0.98 1.01 0.98 0.04
6.19 4.48 1.05
2.09 3.92 0.04 0.98 1.01 0.98 0.04
2.09 3.92 0.04 0.98 1.01 0.98 0.04
1.73 4.31 -0.11 1.09 0.98 1.09 -0.11
1 2.05
1 1.05
0
0
0
0
0
0
0
11.32 3.06
6.96 2.92
6.96 2.92
11.73 2.99
6.96 2.92
6.96 2.92
7.09 3.26
REFERENCES 1. Fai Wong DCH, Mao Yu Hang, Dong Ming Chui. A flexible example annotation schema: translation corresponding tree representation. Proc. 20th Int. Conf. on Computational Linguistics (COLING-2004), Switzerland, Geneva, 2004, pp. 1079-1085. 2. Li Yiping, Pun Chiman, Wu Fei. Portuguese-Chinese machine translation in Macao. Proc. of Machine Translation, SUMMIT VIT'99, Singapore, 1999, pp. 236-243. — 312 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanyo, Hainan, China ©2006 Tsinghua University Press & Springer
CSAT: A Chinese Segmentation and Tagging Module Based on the Interpolated Probabilistic Model Ka Seng Leong1*, Fai Wong1,2, Chi Wai Tang2, Ming Chui Dong1'2 1
Faculty of Science and Technology of University of Macau, PO Box 3001, Macau SAR, China INESC Macau, Macau SAR, China Email: {sejohnny, derek, kevin, dmc}@inesc-macau.org.mo 2
Abstract Chinese is a challenging language in natural language processing. Unlike other languages like English, Portuguese, the first step in Chinese text processing is the segmentation because there are no delimiters in a Chinese sentence for identifying the words boundaries in it. And there are many ambiguity problems during Chinese processing like segmentation ambiguities, unknown words problem, part-of-speech ambiguities, etc. In segmentation and tagging, one of the main tasks is to identify unknown words and recognize proper nouns. In the research, efforts are being paid on this particular problem. In this paper, an integrated application with segmentation and tagging ability has been studied and implemented. In the segmentation, a line of Chinese text is first split up into a sequence of atomic characters. Like this Chinese statement, IfefP^iJT^ (we go to play ball) is split up into S, ff5 i JT i^c with spaces and then for every atomic character in this statement, we are going to search through a knowledge base (necessary statistics about a segmented and tagged Chinese corpus, PFR corpus provided at http://www.icl.pku.edu.cn) to find all the words beginning with those atomic characters and keep this data in an appropriate structure. After that, a depth first search is performed on the data got to generate all the possible segmentations for the Chinese statement based on the words bi-gram model. Upon getting the results, all the candidates are evaluated and the N-best candidate segmentations are selected. In the second phase, an interpolated probabilistic tagging model proposed in [2] with proper nouns recognition and tagging is applied for tagging the N-best candidate segmented Chinese statements. Experiments based on different parameters (e.g., the parameter N used for getting N-best candidate segmentations) were taken for comparison so as to improve the performance of the application. This application is the first step for Chinese processing and it is used as a preprocessing module in the Chinese to Portuguese machine translation system. REFERENCES 1. Zhang Hua-Ping et al. Chinese lexical analysis using hierarchical hidden Markov model. Second SIGHAN workshop affiliated with 41th ACL, Sapporo, Japan, July, 2003, pp. 63-70. 2. Wong Fai, Chao Sam, Hu Dong Cheng, Mao Yu Hang. Interpolated probabilistic tagging model optimized with genetic algorithm. Proceedings of the Third International Conference on Machine Learning and Cybernetics, Shanghai, China, 2004, 2569-2574.
— 313 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanyo, Hainan, China ©2006 Tsinghua University Press & Springer
Development of a Knowledge Based System for the Portuguese Code for Building Acoustics Joao Mariz Graca **, Jorge Patricio 2, Luis Santos Lopes 3 1
Lusiada University, Lisboa, Portugal LNEC, Av. do Brasil, 101, 1700-066, Lisboa, Portugal Acustiprojecto Lda. [email protected], Lisboa, Portugal Email: [email protected] 2
Abstract A knowledge based system for the Portuguese code for Building Acoustics is under development. The system is being developed using XPCE/SWIPROLOG language. This specific PROLOG interpreter was choosen because it provides both: An object oriented architecture linked to PROLOG and a good interface to grapical objects. The XPCE Architecture is not PROLOG, however it is linked to PROLOG and providing a very complete set of libraries for (graphical) user interfacing (GUI). It also provides object oriented (OO) techniques, which are very well suited to handle the complexity of GUI components. Since we are dealing with buildings and architectural shapes, GUI libraries were found very useful to implement the 3D routines that can provide friendly 3D images so that the user can check if he is doing well. The system provides calculations for the following acoustic parameters: 1) airborne sound transmission through adjacent rooms and flanking contributions; calculation of Dn,w parameter, according to EN ISO 12354 standard; 2) impact sound transmission through adjacent rooms and flanking contribution;calculation of L'n,w parameter, according to EN ISO - 12354 standard; 3) sound insulation of facades; calculation of D2m,n,w parameter; 4) reverberation time according to Sabine and Eyring Formulas. The system provides a 3D interface to the user so that he can watch the rooms in which the acoustic field is being studied. The system uses object oriented techniques to provide construction elements that can be used in several different situations. This option was choosen because it seemed similar to designing procedures for buildings. In fact, building designers aim to rationalise projects, simplifying their options by choosing as few types of construction elements as possible. Dispite the fact that the same construction element can be used for different room configurations, only solutions that comply with regulations can be used. Artificial Inteligence (AI) techniques are used at several levels inside the system, such as: 1) to recognise the shapes of the adjacent rooms and choose the correspondent appropriate dimensions and algorithms for calculation; 2) to impose some constraints to the 3D editor so that transmission between two rooms only can exist if they are adjacent and separated by a wall or floor; 3) to ensure that the user selected options are as much consistent as possible. For instance if a flexible element is selected only types of joints for flexible walls can be selected. Since the system is developed under the Prolog language, many other AI techniques and routines where largely applied within the code. The system provide a good interface to the user since he can see 3D images of the parts of the building under acoustic simulation. He also can be confident of the results obtained since AI techniques are used to ensure consistency of the simulations The link between AI and object-oriented techniques was found very usefull to implement this system particularly when dealing with 3D objects. — 316 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Earthquake Response Analysis and Energy Calculation Based on Wavelet Transform Chen Wu *, Ruizhong Zhou College of civil engineering and architecture, Fuzhou University, Fujian, Fuzhou,3 50002 China Email: [email protected] Abstract In earthquake engineering, Fourier transform is a main way for spectrum analysis in the past. However, signal is requested to be stationary and the result couldn't offer time-frequency local character. Therefore, Fourier transform isn't suitable for dealing with seismic signal. Wavelet transform is a perfect way to analyze non-stationary signal for its multi-resolution nature. Any seismic signal can be decomposed to some frequency channels by multi-resolution analysis. Using this method, formulas for earthquake responses of MDOF system are deduced in this paper. Seismic signal and displacement energy in distinct frequency channel are discussed. With examples on MDOF system, an argument that in elastic system total earthquake responses can be obtained by adding all of the dynamic response contributions in distinct frequency channel is demonstrated and the reconstruction signal after restraining high frequency is applied to an approximate model. With energy distribution, dynamics response contributions of distinct frequency channel are analyzed. At the end of this paper, some problems about wavelet transform are discussed. tmmpvditq
GonpoiiMa mamiu
itff toior db|*i£flfMrt6
Bjft.
-4W
OR
1"%
r
,
.*
if
-*«^/l]^v^~vra
lunjui
.^^„.■
a
[ V/^V^v^w
-02, &0S1
id
V%«*V'~v*--"H
son
*■'.*:■:;
a ' V ^ V ' v f ' : i T ' : : - ^ ' ^ : ' : - ■*■■
Figure 1: Components wavelet of distinct frequency Figure 2: Energy distributions of seismic signal and channel and corresponding displacements displacement signal in distinctfrequencychannel REFERENCES 1. Eysa Salajegheh, Ali Heidari. Time history dynamic analysis of structures using filter banks and wavelet transforms. Computers and Structures, 2005; 83: 53-68. 2. Wu Delun, Zhao Mingjie. A preliminary research on wavelet analysis applied to the response of structures. Acta Mechanica Solida Sinica, 1999; 20(s): 174-177 (in Chinese). 3. Jiang Jianguo, Zhou XH, Zou YS, Duan SW. Application of wavelet analysis to degree of single freedom dynamic system. Journal of Hunan University, 2002; 29 (5): 104-109 (in Chinese). — 321 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Effect of Pier and Abutment Non-Uniform Settlement on Train Running Behavior Jianzhen Xiong *, Hanbin Yu, Mangmang Gao China Academy of Railway Science, No.2 daliushu Road, Haidian district, Beijing, 100081 China Email: [email protected], [email protected], [email protected] Abstract Dynamic behavior of running vehicle on bridge is influenced by the attached irregularity of track caused by pier and abutment non-uniform settlement. In order to study the relationship between them, vehicle-track-bridge vertical coupling system dynamic model is established, in which the four-axle car with two suspension systems on independent bogies is adopted, the bridge is simulated with various finite elements. The vehicle components are treated as rigid bodies, assembled with linear springs and dampers. There are totally 10 degrees of freedom, with car body and each bogie having 2 degrees of freedom of vertical and pitching movements, and each wheel-set having 1 degrees of freedom of vertical movement. As one part of track irregularity, the attached deflection is determined by static mechanics. Dynamic analysis uses time domain method, and nonlinear elastic hertz contact theory is adopted in wheel/rail vertical direction, at the same time the wheel/rail deviations can be considered. Based on ballast track and prestressed concrete box girder bridges with 40m span, the homemade Pioneer within 160~220km/h, pier and abutment non-uniform settlement with 5mm, 10mm and 15mm taking into account respectively, the car body acceleration and Sperling index corresponding to different settlement at various running speed are obtained, which can provide a reference to the practice engineering design of railroad bridge. REFERENCES 1. Zhang Geming. Vehicle-Track-Bridge System Dynamic Analysis Model and Track Irregularities Control on Quasi & High-Speed Railway. Doctor Thesis of China Academy of Railway Science, 2001 (in Chinese). 2. Gao Mangmang. Studies on Train-Track-Bridge Coupling Vibratiion and Runnablility of Train on High-Speed Railway Bridges. Doctor Thesis of China Academy of Railway Science, 2001 (in Chinese). 3. Zhai Wanming. Vehicle-Track Coupling Dynamics. China Railway Publishing House, 2002.
— 334 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Elastoplastic Impact of the Sphere upon the Uflyand-Mindlin Plate I. A. Lokteva**, A. A. Loktev2 1
Voronezh State University, Voronezh, Moiseeva 47-134, 394055 Russia OOO "Konmark", Voronezh, 394000 Russia Email: [email protected]
2
Abstract The present paper is devoted to mathematical modeling of the low velocity impact of a sphere on a thin elastic isotropic plate, whose dynamic behaviour is described by the Uflyand-Mindlin equations taking the rotary inertia and shear deformations into account and, therefore, these equations are wave equations. They allow to assume that in a plate the transient wave of transverse shear, because of which there is a deformation of a plate material outside of the contact area, is generated with final velocity. As a method of the decision the ray method and method of splicing asymptotic expansion received for small times in the contact area and outside of it are used. In the present work, the procedure similar to the one proposed in [1] for the analysis of transverse impact of a solid sphere upon an elastic buffer positioned on an elastic orthotropic plate, is used to the case of shock interaction of a solid body in view of a rod with a elastic isotropic plate. The local deformations in the contact region are taken into account in terms of two elastoplastic models and the Hertz's theory. During the interaction of the indenter with the plate, a quasitransverse waves representing the surfaces of strong discontinuity begin to propagate, and the reflected wave has not had time to return to the boundary of the contact disk before the impact process completion. In the plate of the surface of strong discontinuity represent cylindrical surfaces - strip, whose generators are parallel to the normal to the median surfaces and guides locating in the median surface are circumferences extending with the normal velocities. Behind the wave fronts, the solution is constructed in terms of one-term ray expansions [2] whose coefficients are the discontinuities in time-derivatives of the required functions. To determine the desired values inside contact area the equations of motion the impactor and the region of bar's contact with the plate are used. The dynamic characteristics are determined at splicing on border of the contact area of the solution for required function inside a contact disk and outside of it. As a result, we are led to a system of two linear differential equations in the dynamic displacements of plate and the quasi-static strain of the plate material in the contact region. The solution of these equations is found numerically by iteration Timoshenko scheme on computer, and the time-dependence of the contact force is obtained. The carried out numerical researches allow to make the conclusion about influence of parameters of a construction, including plate's elastoplastic properties in the contact region, on dynamic characteristics of interaction. One-term ray series for the desired functions have allowed one to calculate with the given accuracy the stresses in the contact area of the plate and the dynamic safety margin of the thin plate. REFERENCES 1. Loktev AA. Elastic Transverse Impact on an Orthotropic Plate. Technical Physics Letters, 2005; 31 (9): 767-769. 2. Rossikhin YuA, Shitikova MV. A ray method of solving problems connected with a shock interaction. Acta Mechanica, 1994; 102: 103-121. — 322 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
In-Plane Vibrations of Rectangular Plates with Rectangular Cutouts I. Shufrinl, M. Eisenberger!'2* 1
Faculty of Civil Engineering, Technion - Israel Institute ofTechnology, Haifa, 32000 Israel Department of Building and Construction, City University of Hong Kong, Hong Kong, China Email: [email protected], [email protected] Abstract This work presents highly accurate numerical calculations of the natural frequencies and modes for the in plane vibrations of rectangular plates with rectangular cutouts. The solutions are obtained using the multi term extended Kantorovich method. The solution is sought as the sum of multiplications of two one dimensional functions. In this method a solution is assumed in one direction of the plate, and this enables to transform the coupled partial differential equations of the plate equilibrium into an a set of ordinary differential equation. These equation are solved exactly by the exact element method [1], and an approximate natural frequency is obtained. In the second step, the derived solution is now taken as the assumed solution in one direction, and the process is repeated to find an improved approximation of the natural frequency. This process converges with a small number of solution cycles. For plates with cutouts this process yields very accurate values even with 1 term expansion, and in some cases one can improve these values by adding additional functions in the expansion. As an example the natural frequencies of a square plate fully restrained along all four edges, with centrally located square cutout are given in the Table. The size of the cutout is 0.4 of the edge size. The first 5 frequencies of vibration are given together with the results from a finite element analysis using ANSYS (with 8520 DOF). Many more results will be given. Table: Comparison of results with FEM analysis by ANSYS Present
ANSYS 8520 DOF
1 term
2 terms
3 terms
4.369
4.609
4.403
4.378
4.467
4.545
4.480
4.471
4.467
4.545
4.481
4.472
4.546
4.541
...
___
5.426
5.443
5.426
""'
REFERENCES 1. Shufrin I, Eisenberger M. Stability and vibration of shear deformable plates - first order and higher order analyses. Int. J. Solids Structures, 2005; 42: 1225-1251.
— 329 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Interfacing Vision System with Robot for Pick and Place Operation R. Lalitha * Department of Mechanical Engineering, College of Engineering Guindy, Anna University, Chennai, India Email: [email protected] Abstract It is very expensive for a company to have to set up a factory line so that parts are presented in the exact same position to a robot over time. A non-vision -enabled robot will crash or miss if it goes for a part and comes up empty. This can result in a costly and time-consuming line shutdown or manual intervention. To over come this draw back, amore sophisticated system is required. This paper deals with vision -enabled robots. Vision-enabled robot system has a camera for capturing images of components as they travel, software for identifying and processing those images, and lighting to make sure the camera captures the best possible image. The software runs on a Windows-based computer connected to an Ethernet network. Instead of locking a part's position in advance to suit a blind robot, the camera in a vision-enabled robot lets the robot see the position of a loose part and adjust itself accordingly to manipulate it. The main objective of this work is to develop a system to see the component position, calculate the component's position, grasp it, inspect it, and move it to where it needs to go. Robot vision may be defined as a process of extracting, characterizing and interpreting the information from the images. The system comprises of a 5-axis robot driven by its own controller. In this work we use CCD (charge coupled device) camera for capturing the two-dimensional image of the scene where the objects to be picked up lie. CCD camera discretizes the scene into a 752 * 552 format, which can be stored in the RAM of a computer. The information from the CCD camera is processed by an image processing card mounted within the computer. The view area is digitized using VB 6.0 so that the coordinate values of any object in this area are found out. NI Vision Builder for Automated Inspection software is used for processing the image (geometric matching, Shape and colour analysis) and to find out the center of gravity of the object and its orientation. It can communicate triggering and inspection results directly to NI M Series DAQ devices or to industrial devices over serial and Ethernet protocols. It also includes the ability to set up complex pass/fail decisions to control digital I/O devices and to communicate with serial device like robot. Interfacing card is used for connecting the computer to the robot. Values are send to the robot via I/O card, which makes the robot to position its gripper accordingly in order to pick up the object and move it to the required destination.
— 317 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Interval Dynamic Analysis Using Interval Factor Method Wei Gao* School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney, NSW 2052, Australia Email: [email protected] Abstract The dynamic analysis of structures with uncertain parameters is a very significant research field in engineering [1-3]. Recently, the interval analysis method has been used to deal with the static response, natural frequencies and dynamic response of structures with bounded uncertain (interval) parameters [4-5]. In their studies, several important results have been obtained by using interval analysis and matrix perturbation techniques. In perturbation methods, the uncertainty of all the structural parameters are expressed as small parameters in the structural mass and stiffness matrices. These small parameters are not interval variables, but simply small values. Therefore, their methods can not reflect the effect of the uncertainty of the individual parameters on the structural analytical results. A new method called the interval factor method (IFM) for the natural frequency and mode shape analysis of truss structures with interval parameters is presented in this paper. Using the IFM, the structural physical parameters and geometric dimensions can be considered as interval variables. The structural stiffness and mass matrices can then be respectively divided into the product of two parts corresponding to the interval factors and the deterministic matrix. The computational expressions for the midpoint value (mean value), lower bound, upper bound and interval change ratio of the natural frequency and mode shape are derived from Rayleigh quotient by means of the interval operations. The influences of the change of the structural parameters on the natural frequency and mode shape are demonstrated by using truss structures. REFERENCES 1. Stefanou G, Papadrakakis M. Stochastic finite element analysis of shells with combined random material and geometric properties. Computer Methods in Applied Mechanics and Engineering, 2004; 193: 139-160. 2. Liu Q, Rao SS. Fuzzy finite element approach for analysis of fiber-reinforced laminated composite beams. AIAA Journal, 2005; 43: 651-661. 3. Moens D, Vandepitte D. A survey of non-probabilistic uncertainty treatment in finite element analysis. Computer Methods in Applied Mechanics and Engineering, 2005; 194: 1527-1555. 4. Chen SH, Yang XW. Interval finite element method for beam structures. Finite Elements in Analysis and Design, 2000; 34: 75-88. 5. Qiu ZP, Wang XJ. Parameter perturbation method for dynamic responses of structures with uncertain-but-bounded parameters based on interval analysis. International Journal of Solids and Structures, 2005; 42: 4958-4970.
— 332 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Limit State Analysis of Seismically Excited 3D R/C Beam Bearing Structures N. Kaufmann * Bauhausstrafie 4, 99423 Weimar, Germany Email: [email protected] Abstract Based on the capacity design method in [1] a calculation model is presented which enables the analysis of plane r/c frameworks using linear and quadratic optimization algorithms. In this connection, as criterion for evaluation the ultimate limit (shakedown) state, the adaptive load factor p A is defined. An extended and modified calculation model using non-linear optimization algorithms will be introduced, which allows the ULS analysis of 3D frameworks considering realistic non-linear plasticity conditions for the first time [2]. The plasticity conditions describe the interaction between the axial force and the bending moments of a 3d beam element. It is important to consider the additive division of the internal forces into a linear elastic part SE and into an irreversible residual-stress part SR. The elastic part is calculable using linear-elastic dy namic models, separated from the non-linear analysis. The reducing of the elastic solution SE to extreme combinations se is recommendable to ensure a restricted number of plasticity conditions. The determina tion of the combinations se results in dependence of the developed criterion of minimal load intensity p. This procedure allows the inclusion both linearly as well as non-linearly defined plasticity conditions. With an example of a three-dimensional framework subjected to TAFT-earthquake will be quantified the influ ence both of the formulation of the plasticity restrictions and of the determination of the linear elastic com binations SE on the results of the adaptive load state. Table 1: Calculation model for limit state analysis Determination of residual forces p < p A
Determination of adaptive load factor p A
Determination of adaptive resistance factor rA
Objective function
—SpQ s R => Minimum
p => Maximum
r => Minimum
Restrictions
A
A
G
S
S
R
A
= 0
b
b
P R^ p- ePJ
A
S
b
b
P R^l p- ePj
G
S
R
= 0
A p s R
REFERENCES 1. Schiiler H. Zur Analyse und zur Bemessung adaptiver Tragwerke aus Stahlbeton unter dynamischen Einwirkungen. Dissertation, Bauhaus-Universitat Weimar, Germany, 1997. 2. Kaufmann N. Physikalisch nichtlineare Analyse dreidimensionaler Stabtragwerke aus Stahlbeton mit der Methode der mathematischen Optimierung. Dissertation, Bauhaus-Universitat Weimar, Shaker Verlag, Aachen, Germany, 2003.
— 320 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X,Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Numerical Analysis of Impact between Cue and Ball in Billiard (Effect of Tip Structure) Shinsuke Shimamura**, Shigeru Aoki 2 1
Graduate School of Engineering. Sci. Eng., Toyo University, Kujirai 2100, Kawagoe, Saitama 350-8585, Japan 2 Dept. ofComp. Sci. Eng., Toyo University, Kujirai 2100, Kawagoe, Saitama350-8585, Japan Email: [email protected], [email protected] Abstract A finite element analysis and an experiment on the impact between a cue and a ball in billiard are carried out. It is assumed that the cue is elastic and the ball is rigid. The displacement of the cue is calculated by FEM and that of the ball is estimated by solving the equation of motion. The contact force is determined by equating the sum of these displacements to the impact velocity times duration. An experiment, in which a freely supported cue is hit with a swinging ball, is performed to examine the accuracy of the analysis. It is shown that (1) the computational results on the time variation of contact force agree well with the experimental ones, (2) the contact period is reduced by mounting the plastic collar near the tip of the cue, and (3) the contact force rises steeply with the mounted plastic collar. REFERENCES 1. Aoki S et al. Transactions of the Japan Society of Mecanical Engineers, A 2002; 68(670): 81-83. 2. Toda S. Mechanics. Iwanami Shoten, Tokyo, 1994 (in Japanese).
— 323 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanyo, Hainan, China ©2006 Tsinghua University Press & Springer
Optimal Control of Temperature Gradient in a Large Size Magnetic Czochralski Silicon Crystal Growth by Response Surface Methodology H. P. Yu l*9 Y. K. Sui \ J. Wang2, X. L. Dai 2 , G P.Anl 1
Numerical Simulation Center of Engineering, Beijing University of Technology, Beijing, 100022 China General Research Institute for Nonferrous Metals, Beijing, 100088 China Email: [email protected] Abstract Numerical simulation of a Czochralski crystal growth is a very helpful tool in optimizing the real experiment to produce high-quality single crystals in microelectronic industry. With the increase of silicon crystal size by Czochralski method, the melt volumes and the corresponding crucible diameters have to increase as well, which make the melt flows become more and more turbulent, laminar model is no longer suitable, so a low-Reynolds number k-e model of Jones and Launder considered Lorentz force were used to describe a large-scale crystal growth process in this paper. The SIMPLE algorithm was employed to couple velocity and pressure field. A finite volume method was employed and a staggered grid arrangement was used to avoid zigzag pressure field. A third order QUICK (Quadratic Upwind Interpolation of Convective Kinematics) was used to discretize the convection term in the governing equations. In order to get low defects crystal ingot, the growth interface should be kept flat or slightly concave. This means that the isotherm at the growth interface is approximately perpendicular to the growth direction, the isotherm should be flatter, and the small temperature gradient at the interface is suitable. While the temperature gradient is strongly influenced by the flow pattern in the crucible, the strength of the magnetic field, the crystal and crucible rotations are the three major factors in determining the melt flow pattern, in this study, we aim at optimizing this three design variable to control the temperature gradient at the interface. Concepts and techniques of response surface methodology (RSM) have been widely applied in many branches of engineering, especially in the chemical and manufacturing areas. The basic idea of RSM is to approximate the actual state function, which may be implicit and/or very time-consuming to evaluate, with the so-called response surface function that is easier to deal with complex problem. This paper presents an application of the methodology with a turbulence model to optimize the temperature gradient. The simulation demonstrates that the response surface methodology is a feasible algorithm for the optimization of the Czochralski crystal growth process. REFERENCES 1. Lipchin A, Brown RA. Comparison of three turbulence models for simulation of melt convection in Czochralski crystal growth of silicon. J. Cryst. Growth, 1999; 205: 71-91. 2. Jones WP, Launder BE. The prediction of laminarization with a two-equation model of turbulence. Inter. J. Heat and Mass Transfer, 1972; 15: 301-311. 3. Redhe M, Forsberg J, Jansson T, et al. Using the response surface methodology and the D-optimality criterion in crashworthiness related problems. Struct. Multidisc. Optim., 2002; 24: 185-194.
— 330 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Overcoming Data Sparseness Problem in Statistical Corpus Based Sense Disambiguation Francisco Oliveira*, Fai Wong, Anna Ho, Yiping Li, Mingchui Dong Faculty of Science and Technology, University of Macau, Macao, China Email: {olifran, derekfw, ma36560, ypli, mcdong}@umac.mo Abstract The problem of data sparseness is considered as a common problem for Statistical Corpus based Sense Disambiguation approaches [1]. Usually large amounts of data are required in the corpus to guarantee that all senses of an ambiguous word are presented. However, this is not easily achieved, especially for words that do not occur frequently in the training corpus. On the other hand, for languages that do not have large amount of digitized resources, the sparseness problem is even worse. In this paper, we present an unsupervised framework that first learns the relationships between the ambiguous and related words to reveal their most suitable senses based on a proposed mathematical model and a set of bilingual resources, including a non-aligned Portuguese-Chinese training corpus, a dictionary, and a sense inventory. For senses not found in the learning phase, bilingual examples from the dictionary and Singular Value Decomposition [2] techniques are applied to overcome the sparseness problem. It is believed that the examples in the bilingual dictionary can reflect the most suitable meaning and sense of each word. Thus, these can be taken into consideration for learning extra senses that do not occur frequently in the training corpus. For each example related to the ambiguous word, the proposed method will identify their corresponding related words based on a defined context window, relative distance and their mutual information. These words in the source language example are then aligned with the ones extracted from the target language for identifying new senses. Words related to an ambiguous word often have a strong relationship between each other. If these are ambiguous words, then extra relationships can be found. This is modelled by a vector space, a matrix of related words by the senses of the ambiguous word. A vector for a word v is derived from the set of words related to the ambiguous word w. Each entry in the vector represents the number of times that v occurs with one of the senses of w in the corpus. The closeness between vectors is determined by the cosine of the angle between the vectors. Singular Value Decomposition is applied in this vector space to overcome the sparseness problem and to further explore the relationships between words in the matrix. All the senses found are converted into a set of rules and stored in the Word Sense database for later use in disambiguation and translation process. Preliminary experiment results show an improvement of learning more senses in the sparseness environment with the use of the mentioned strategies.
REFERENCES 1. Ide N, Veronis J. Introduction to the special Issue on word sense disambiguation: the state of the art. Computational Linguistics, 1998; 22(1): 1-40. 2. Gene H Golub, van Loan Charles F. Matrix Computations. The Johns Hopkins University Press, Baltimore and London, 1989.
— 314 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Sensibility Analysis of Violin Plates Mario Razeto*, Claudia Staforelli, Gabriel Barrientos Departamento de Ingenieria Mecdnica, Universidad de Conception, Casilla 160 C- Conception, Chile Email: [email protected] Abstract The study of dynamic and vibratory behavior of violins considers the effect of the different parts that compose it. The top and back plates have great importance in the transmission of vibrations and the characteristic tone of the violin; therefore, the study is centered in their vibratory behavior, since the ideal form of the vibrational modes and frequency of violins of greater prestige is known, according to bibliography. Modal Analysis Experimental tests determine the vibrational modes with their resonant frequencies of the violin plates. A numerical model of the top plate is made by means of the finite elements method, to determine the influence of the different mechanical and geometric properties on its main vibrational modes and natural frequencies; with the objective of obtaining the expected acoustic response, making precise changes in their structure. The height in the arching of the plates is modified to obtain different effects on the frequencies and the vibrational modes. A sensibility analysis is applied on a finite elements model of the top plate, to determine the influence of the thickness in different zones on its natural frequencies, and to study the effect produced by the thickness variations of the bass bar. With an optimisation study the thickness distribution is modified to obtain the ideal natural frequencies and achieve the right vibratory behaviour, with a similar dynamic response as violins of greater prestige.
— 333 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X,Aug. 21-23, 2006, Sanya, Hainan, China ©2006 Tsinghua University Press & Springer
Simplified Doubly Asymptotic Approximation Boundary for Foundations Dynamic Analysis Wenjun Lei, Demin Wei * College ofArchitecture and Civil Engineering, South China Univ. of Tech., Guangzhou, 510640 China Email: [email protected] Abstract The paper presents a simplified doubly asymptotic approximation boundary (spring-viscous boundary) for infinite medium used in finite element method, which can be applied to both static and dynamic foundation problems. The boundary can be realized by using special boundary elements. The spring part of this boundary can be determined by Mindlin Equations, and frequency dependent viscous material (resistance proportional to velocity) is introduced into the boundary elements to simulate dashpots of the viscous boundary. When choosing appropriate parameters of Young's modulus, Poisson's ratio and material damping ratio, these boundary elements can simulate not only the elasticity recovery capacity of the far field media, but also the radiation damping. Two case studies justify the validity and practicability of this simplified boundary, which proves that it is applicable to the dynamic soil-structure interaction analysis.
Figure: Flexibility functions F\ and F2 REFERENCES 1. Veletsos AS, Verbic B. Vibration of viscoelastic foundations. Earthquake Engineering and Structural Dynamics, 1973; 2(1): 87-102. 2. Underwood P, Geers TL. Doubly asymptotic, boundary-element analysis of Dynamic soil-structure interaction. Journal of Solid and Structures, 1981; 17(8): 687-697. 3. Engquist B, Majda A. Absorbing boundary conditions for the numerical simulation of wave. Math. Comput, 1977;31:629-651. — 319 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan,China ©2006 Tsinghua University Press & Springer
Three-Dimensional Vibration Analysis of Functionally Graded Material Rectangular Plates by Chebyshev Polynomials Q.Li*,V.P.Iu,K.P.Kou Department of Civil and Environmental Engineering, University of Macau, Av. Padre Tom 'as Pereira S. J., Taipa, Macao SAR, China Email: [email protected] Abstract Functionally graded materials (FGMs) are generally two-phase composites with continuously varying volume fractions. This advantage of continuousness can eliminate interface problems of composite materials. In this paper, threedimensional vibration analysis of FGM rectangular plates has been investigated. Consider the case of a uniform thickness, FGM rectangular plate simply supported along the four edges. The volume fraction of the FGM properties is assumed to obey a power-law function along the thickness direction. However, the Poisson's ratio is assumed to be constant for the effect of Poisson's ratio on the deformation is much less than that of Young's modulus. The three mechanical displacements components of the plate are expanded in triplicate series of Chebyshev polynomials multiplied by the boundary R-function which makes expansions satisfy the essential boundary conditions along the edges. Chebyshev polynomial series are chosen as admissible functions for they are a set of complete and orthogonal series in the interval [-1/1], The Lagrangian function L of the plate is expressed in terms of Chebyshev polynomial series. By Ritz method, the partial differential of Lagrangian function L with respect to independent coefficients leads to a set of linear equations in form of eigenvalue matrix for natural vibration frequencies. The mode shapes corresponding to each eigenvalue may be obtained by back substitution of the eigenvalues one by one in the usual manner. In present study, rectangular FGM plates with four simply supported edges are taken as examples for the convergence study. The trial plates are of different volume fraction exponents and thickness-side ratios. The convergence studies reveal the rapid convergence rate and high efficiency. The frequencies monotonically decrease and approach certain values with the increase in the number of terms of admissible functions. Three terms are sufficient for the requirement of expansion in the thickness direction to obtain the first twenty natural frequencies. It is also found that the convergence rate is independent of volume fraction exponents k values of FGMs. In the last part of this paper, two comparisons have been carried out to validate the present method. The numerical results of the first eight natural frequencies of simply supported square FGM plates are compared with the solutions of the higher-order shear and normal deformable plate theory for two special cases of isotropy; the natural fundamental frequency parameters of simply supported square FGM plates with different thickness-side ratios are compared with the solutions of finite element method. In the modeling of finite element analysis, there is an simplification of material definition for the material properties variation along the thickness of the plate. The relative thick plate and thin plates are meshed by solid and shell element types according to their thickness-side ratios, respectively. It is seen that both comparisons show good agreements. The method presented in this paper is a good and valid approach in analyzing the rectangular FGM plates.
— 326 —
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan,China ©2006 Tsinghua University Press & Springer
Vibration Assessment of Railway Viaducts Under Real Traffic Using Bridge-Track Models Constan9a Rigueiro1, Carlos Rebelo2*, Luis Simoes da Silva2 1
Department of Civil Engineering, Institute Polytechnic ofCastelo Bronco, Portugal Department of Civil Engineering, University ofCoimbra, Portugal Email: [email protected]
2
Abstract Among the several safety checks that must be performed during the design of small to medium single span railway viaducts, the one concerning vertical accelerations is often crucial for high speed railways, since under these conditions resonance is much likely to occur. Recent results [1-3] of several field measurements carried out on simply supported medium span concrete railway viaducts showed that the non-linear behaviour of the superstructure composed by ballast and rails can play an important role in the dynamic behaviour of the structure and consequent evaluation of its maximum vertical accelerations. The conclusions drawn from those measurement results pointed out that the superstructure must be taken into account in the numeric analysis of small to medium span bridges, mainly what global ballast-structure damping is concerned. This revealed to be particularly important when decisions are to be taken, related to the strengthening of existing structures in order to increase traffic speeds and when comfort of passengers is an important issue. In order to evaluate the vertical vibrations of the bridges when the dynamic behaviour of the track is taken into account, same authors have already proposed different models including vertical springs, dampers and masses, which are interpose between loads and structure in order to simulate the railway track behaviour. These models include the rail with flexural stiffness in vertical and lateral direction and axial stiffness in longitudinal directions, the rail pads as vertical springs and dampers, the sleepers as rigid bodies with masses, and finally the ballast as springs and dampers. The main purpose of this paper is to compare the dynamic behaviour of ballasted simple supported viaducts with and without the referred track models, taking into account the structural dynamic response obtained from the field measurements, in order to evaluate the influence of the track in the safety check. Furthermore, the response acceleration of the ballasted simple supported viaducts is also compared with the results obtained from the simplified methods proposed by the ERRI D214 Committee used to estimated the maximum acceleration at mid-span of simply supported bridges decks, namely the DER Method (Decomposition of Excitation at Resonance Method) and the Virtual Influence Line Method.
REFERENCES 1. Rebelo C, Heiden M, Pircher M, Simoes da Silva L. Vibrations measurements on existing single-span concrete railway viaducts in Austria. EURODYN 2005, Paris, 2005, pp. 1637-1642. 2. Rigueiro C, Rebelo C. Simoes da Silva L, Pircher M, Heiden M. Dynamic behaviour of ballasted single railway bridges. Metodos Numericos en Ingenieria 2005, Granada, 2005. 3. Rebelo C, Simoes da Silva L, Pircher M, Rigueiro C, Heiden M. Vibrations measurements on small to medium single-span railway bridges. Experimental Vibration Analysis for Civil Engineering Stuctures - EVACES, Bordeaux, 2005. — 328 —
Author Index
* denotes the presenter of the paper
Agelet de Saracibar C
*247
Dai XL
330
Al-Falahi A
♦180
Dang XH
294
Amaya K
288
DasS
AnGP
330
De Bortoli AL
AokiS
191,285,288,323
Asami T
♦173
♦196 ♦184,243
Deeks AJ
255, 256, + 257
Denda M
♦270,271
Asayama T
195
DiSK
294
AuSK
206
Ding GF
300
Aubry D
209
Doltsinis I
♦35
BarnatW
223
Dong MC
258,272,313,314,315
Barrientos G
333
Dong ZZ
Bento R
230
DuY
♦251
Brou5ek M
295
DuYF
♦294
CaiMF
245
DuZF
202
♦250,251
Duan J
♦215
Eisenberger M
♦329
CenS CenZZ
219,265
Cervera M
247
Cescotto S
*1
FanWB
179
FengX
ChaiG Chai JR
♦291
Ezawa Y
Feng XQ
Chan IN
190
FuDJ
Chan SL
258
Fujisawa T
Cheang TS
♦258
Chen CS
113
Chen HB
*261
Chen JG
185
280
274 175 ♦232 268 261 199,200
Fujita D
200
GaoH
268
GaoMM GaoSX
♦229, 334 1
Chen MC
♦231,234
Gao W ( 1 )
♦275
Chen TG
214
Gao W ( 2 )
♦332
Chen WQ
♦327
Ghajar A J
244
Chen XM
250
Gong YB
♦301
Chen XY
♦307
Gong YQ
♦216
ChenY
♦210
Graca JM
Chen YQ
185,*194
GuBQ
♦316 ♦186,210,232,306
Chen ZP
235
GuoXF
261
Cheng YL
283
GuoYT
175
ChewYT
♦181
Chiumenti M
247
Habte MA HanDJ
Choi HF
♦170,172
HanF
Choi LY
♦241
HanX
59 ♦51,286 273 71
Chung MS
248
He EM,
Cong GH
♦187
HeWY
176
273
Ho A N
♦312,314
CuiJZ
— 335 —
324
HoSM HoiKI HongH HouSJ HuWD Huang CK Huang D Huang JJ Huang Y HungMC Ikeda T Inaba M IribeT IuVP JanYJ JiB Jiang JJ JinXQ JungWS Kakimoto K Kanda Y Kandasamy R KangC KangZ Kaufmann N Kawai H Kee BBT Keong WS Khalili N Khatchatourian O KimJM Kiong SC Kobayashi Y Kou KP Kuklik P Kurowski Z Lackner R Lalitha R LamLH Lamas LN Lao MI LaoSK LeiSL LeiT LeiWJ Leitao NS Leong KS
♦290 *259 256, 257 ♦217 202 214 ♦267 181 *218,226 318 88 263 200 326 248 268 204 277 *233 266 200 ♦242 ♦169 35, *308 *320 200 71 241 ♦59 243 153 241 *262 ♦197,326 *295 205 *168 *317 *276 183* *190 170,* 172 190 19 319 183 *313,315
LiBS LiGR LiGY LiH LiHT Li J LiK LiLC LiQ ( 1 ) LiQ ( 2 ) LiQY LiT LiW Li XL LiXQ LiXS LiYP LiYQ LiYZ LiZL LiZY Liang SJ Liang T Liang ZZ Liao XT Lin FY LinJG LinSP Lindig V LiuB LiuD LiuGR LiuR LiuWK LiuX LiuXM LiuY ( 1 ) LiuY (2) LiuYH (1) LiuYH (2) LiuYL LiuYM LiuYN LoKM Lobo Ferreira JP Lok TMH Loktev AA
— 336 —
325 331 71 294 182 287 216 *198 217,302,307 *326 301 225 *211 *260 213 304 314,315 219 194 *188, 189 203 *248 305 198 *302 *220 174 113 *284 309 169 *71 232 *87 221,236 269 *185 305 214, *265 *175 *245 265 *282 1 290, *297, 298 322
Lokteva IA Long SY Long YQ Lopes LS Lopes N LouCW Lourenco N LiiCF, LuXZ LuoDM Luo JJ LuoYF Malachowski J Maranha JR Matsubara H Matsuo Y Mellor BG Meng JJ MengWY MiZK Miao ZW Mirambell E Miyazaki N Mohite PM MokKM Murotani K Nagaoka S Nakabayashi Y Nakanishi T Nielsen MP Niezgoda T Nogueiro P Okada H OkudaH Oliveira F Osaki H PanE PanJY Patricio J Peng XH Peng ZR Pereira E Periasamy K Petry VJ Ping XC Qian HS QieYH
*322 217,307 250 316 *212 ♦272 1 327 *204 *266 51 193, 218, *221, 224, 226, 236 *205 *293 15,201 *177 237 *303 ♦213 *296 204 212 *88 222 259, 276 *199 *263 173, 177 ♦178 179 205, *223 230* *200 260 312,*314 *201 271 229 316 *182 303 228 242 ♦243 231,*234 281 309
QinR QinY Razeto M Rebelo C RenJG RenQW RenQX RidhaM RigoN Rigueiro C Rodrigues HC Rodrigues J Roubens M SangJB Santos LO SatoM Sekar BD Shao YB Shen ZJ Shen ZY Shiau J Shibata H Shijo K Shimamura S ShuC Shufrin I Simoes da Silva L SinVK Sivagnana Prabhu KK Song DP Song HJ SongY Song ZT Staforelli C SugaK SuiYK Sun HI SunLS SunQ SunZ Suzuki H Swoboda G Syngellakis S Takagaki M Takao Y TamHK TamLM
— 337 —
♦331 300 *333 ♦328 208 292 *214 ♦191 ,285,288 1 328 ♦101 238 1 ♦309 238 178 258 *202 296 227 ♦192 178 200 *323 181 329 212,230,328 170,171, 172 242 250 193,*224 294 289 333 *285,288 311,330 *171 ♦299 279 203 *274 219 237 *195 266 ♦244 170, 171 ,172,244
WeiWL
*176
TanT
♦304
Williams FW
*168
TanYP
♦286
Wong CK
244
TamSC
Tang CA
198
Tang CW
313,*315
Tang RW
227
WongF
272 312,313,314,315
WongKI
171
Woon OH
241
Tian ZR
*203
WuAH
♦237
Tian ZS
♦252,253
WuBX
*281
WuC
♦321
WuJY
♦287
TieB
*209
ToiY
195,233
Tong LW
225
WuQX
*207
TouCM
297
WuZR
*283
Upadhyay CS Valliappan S
♦222 59
1
Xiang XM Xiang ZH
2 1 1 , 2 1 5 , *219
Vieira A
293
Xiao JC
♦305
Vieira R
*228
Xiao LJ
235
212
XieJL
234
228 ♦277
XieNG
299
XieZH
*174
VuTH
*255
Xing SF
309
WanS
♦179,281
Xiong JZ
*334
Vila Real PMM Virtuoso F Vong SW
XuCL
Wang AP
*253
Wang CY
270, *271
XuM
Wang DD
254, *264
XuXQ
187
Wang FJ
♦324
Wang HJ
XueMD Yagawa G
♦193,224 ♦238 ♦325 211,215 ♦15, 199, 200, 201, 260, 262, 263
(,)
19
WangHT ( 2 )
♦235
Yang LC
309
WangJ ( 1 )
*206
Yang M
239
WangHT
Wang J
(2)
(3)
245
YanSL
♦239
169
Yang MG +
224, 240
♦318
Yang MW
Wang J ( 4 )
330
Yang MZ
207
Wang JG
*300
Yang QP
252
Wang JX
♦246
YangR
185
WangK
♦225
Yang XJ
Wang MY
♦310
Yang YB
Wang PB
19
Yang YQ
Wang SL
283
Yang ZJ
Wang SM
*278
Yang ZQ
Wang SR
245
Yang ZX
WangT
331
Yanovsky YuG
WangW
277
YaoZH
♦19
Wang WX
266
Yasuyoki K
199
Wang XC
246
YeHL
Wang XD
1
Ye LP
Wang ZB
221, *236
WangJ
Wei DM
*319
Yoshida M YuHB
— 338 —
217,307 ♦113 229 ♦256, 257 303 282 ♦129
♦311 204 ♦288 334
YuHJ YuHP YuR YuTT YuY Yuen KV YunCB YusafT YusoffMZ Zhang AQ Zhang C Zhang CH Zhang JL Zhang K Zhang L Zhang PQ Zhang SJ Zhang T Zhang WG Zhang WH Zhang XQ Zhang Y
*298 *330 218,*226 *292 *273 ♦139,206,259 *153 180 180 1 308 *254 254 280 187 261 *208 269 302 299 252, 253 289
Zhang YJ Zhang YS Zhang YX Zhang ZM Zhao HM ZhaoKZ ZhaoXZ Zheng HW Zheng Y Zhong ZH ZhouJF(1) ZhouJF(2) ZhouJT(1) ZhouJT(2) Zhou MS ZhouRZ ZhuBQ ZhuBS ZhuLJ Zhuang Z Zhuo JS Zou J
*279 278 188, *189 *289 *280 207 *227 181 *168 71 249 *306 1 174 219 321 *249 189 186 ♦269 213,249,267 *268