CMES-Vol. 4, No. 5, 2003

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ARTICLE

Meshless Local Petrov-Galerkin (MLPG) Approaches for Solving the Weakly-Singular Traction & Displacement Boundary Integral Equations
S. N. Atluri¹, Z. D. Han¹, S. Shen¹
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 507-518, 2003, DOI:10.3970/cmes.2003.004.507
Abstract The general Meshless Local Petrov-Galerkin (MLPG) type weak-forms of the displacement & traction boundary integral equations are presented, for solids undergoing small deformations. These MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs [given in Han, and Atluri (2003)], which are simply derived by using the gradients of the displacements of the fundamental solutions [Okada, Rajiyah, and Atluri (1989a,b)]. By employing the various types of test functions, in the MLPG-type weak-forms of the non-hyper-singular dBIE and tBIE over the local sub-boundary surfaces, several types of… More >

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Free and Forced Vibrations of Thick Rectangular Plates using Higher-Order Shear and Normal Deformable Plate Theory and Meshless Petrov-Galerkin (MLPG) Method
L. F. Qian^1,2, R. C. Batra³, L. M. Chen¹
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 519-534, 2003, DOI:10.3970/cmes.2003.004.519
Abstract We use a meshless local Petrov-Galerkin (MLPG) method to analyze three-dimensional infinitesimal elastodynamic deformations of a homogeneous rectangular plate subjected to different edge conditions. We employ a higher-order plate theory in which both transverse shear and transverse normal deformations are considered. Natural frequencies and the transient response to external loads have been computed for isotropic and orthotropic plates. Computed results are found to agree with those obtained from the analysis of the 3-dimensional problem either analytically or by the finite element method. More >

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Some Aspects of the Method of Fundamental Solutions for Certain Biharmonic Problems
Yiorgos-Sokratis Smyrlis¹, Andreas Karageorghis¹
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 535-550, 2003, DOI:10.3970/cmes.2003.004.535
Abstract In this study, we investigate the application of the Method of Fundamental Solutions for the solution of biharmonic Dirichlet problems on a disk. Modifications of the method for overcoming sources of inaccuracy are suggested. We also propose an efficient algorithm for the solution of the resulting systems which exploits the symmetries of the matrices involved. The techniques described in the paper are applied to standard test problems. More >

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Molecular-Dynamics Analysis of Grain-Boundary Grooving in Interconnect Films with Underlayers
T. Iwasaki¹ and H. Miura¹
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 551-558, 2003, DOI:10.3970/cmes.2003.004.551
Abstract We have developed a molecular-dynamics technique for investigating migration-induced failures in interconnect films for ULSIs. This technique was used to simulate grain-boundary grooving in Al and Cu films. The simulations showed that the grain-boundary grooves are formed by atomic diffusion at the grain boundary. To clarify what kind of underlay material is effective in suppressing this diffusion, we calculated the dependence of groove depth on the kind of underlay material. The calculation showed that the groove depth of the Al film decreases in the order: Al/Ta, Al/W, and Al/TiN while that of the Cu film More >

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A Geometric Embedding Algorithm for Efficiently Generating Semiflexible Chains in the Molten State
M. Kröger¹, M. Müller², J. Nievergelt²
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 559-570, 2003, DOI:10.3970/cmes.2003.004.559
Abstract We present a novel method for generating starting polymer structures for molecular simulations in the dense phase. The work describes the ingredients of an algorithm for the creation of large, dense or diluted amorphous polymeric systems close to equilibrium and provides measures for its quality. The model systems are made of semiflexible (wormlike) repulsive multibead chains. The key feature of the method is its efficiency, in particular for large systems, while approaching given local and global chain characteristics. Its output has been proven to serve as an excellent basis for subsequent off-lattice molecular dynamics computer More >

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Application of Meshless Local Petrov-Galerkin (MLPG) to Problems with Singularities, and Material Discontinuities, in 3-D Elasticity
Q. Li¹, S. Shen¹, Z. D. Han¹, S. N. Atluri¹
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 571-586, 2003, DOI:10.3970/cmes.2003.004.571
Abstract In this paper, a truly meshless method, the Meshless Local Petrov-Galerkin (MLPG) Method, is developed for three-dimensional elasto-statics. The two simplest members of MLPG family of methods, the MLPG type 5 and MLPG type 2, are combined, in order to reduce the computational requirements and to obtain high efficiency. The MLPG5 method is applied at the nodes inside the 3-D domain, so that any domain integration is eliminated altogether, if no body forces are involved. The MLPG 2 method is applied at the nodes that are on the boundaries, and on the interfaces of material More >

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A Real-Coded Hybrid Genetic Algorithm to Determine Optimal Resin Injection Locations in the Resin Transfer Molding Process
R. Mathur¹, S. G. Advani², B. K. Fink³
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 587-602, 2003, DOI:10.3970/cmes.2003.004.587
Abstract Real number-coded hybrid genetic algorithms for optimal design of resin injection locations for the resin transfer molding process are evaluated in this paper. Resin transfer molding (RTM) is widely used to manufacture composite parts with material and geometric complexities, especially in automotive and aerospace sectors. The sub-optimal location of the resin injection locations (gates) can leads to the formation of resin starved regions and require long mold fill times, thus affecting the part quality and increasing manufacturing costs. There is a need for automated design algorithms and software that can determine the best gate and… More >

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3-D Transient Dynamic Crack Analysis by a Novel Time-Domain BEM
Ch. Zhang², A. Savaidis³
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 603-618, 2003, DOI:10.3970/cmes.2003.004.603
Abstract A novel non-hypersingular time-domain traction BEM is presented for three-dimensional (3-D) transient elastodynamic crack analysis. The initial-boundary value problem is formulated as a set of non-hypersingular time-domain traction boundary integral equations (BIEs). To solve the time-domain traction BIEs, a time-stepping scheme based on the convolution quadrature formula of Lubich (1988a,b; 1994) for temporal discretization and a collocation method for spatial discretization is adopted. Numerical examples are given for an unbounded solid with a penny-shaped crack under a tensile and shear impact loading. A comparison of the present time-domain BEM with the conventional one shows that More >

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