CMES-Vol. 38, No. 2, 2008

Open Access

ARTICLE

Solutions for periodically distributed materials with localised imperfections
M. Patrício¹, R. Mattheij², G. de With³
CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 89-118, 2008, DOI:10.3970/cmes.2008.038.089
Abstract The behaviour of composite materials with periodically distributed constituents is considered. Mathematically, this can be described by a boundary value problem with highly oscillatory coefficient functions. An algorithm is proposed to handle the case when the underlying periodicity is locally disturbed. This procedure is constructed using fundamental concepts from homogenisation theory and domain decomposition techniques. Applications to layered materials are considered. More >

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ARTICLE

Shared Memory OpenMP Parallelization of Explicit MPM and Its Application to Hypervelocity Impact
P. Huang^1,2, X. Zhang^1,3, S. Ma¹, H.K. Wang¹
CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 119-148, 2008, DOI:10.3970/cmes.2008.038.119
Abstract The material point method (MPM) is an extension of particle-in-cell method to solid mechanics. A parallel MPM code is developed using FORTRAN 95 and OpenMP in this study, which is designed primarily for solving impact dynamic problems. Two parallel methods, the array expansion method and the domain decomposition method, are presented to avoid data races in the nodal update stage. In the array expansion method, two-dimensional auxiliary arrays are created for nodal variables. After updating grid nodes in all threads, the auxiliary arrays are assembled to establish the global nodal array. In the domain decomposition… More >

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A meshfree poly-cell Galerkin (MPG) approach for problems of elasticity and fracture
C. Zheng¹, S. C. Wu^2,3,4, X.H.Tang¹, J. H. Zhang¹
CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 149-178, 2008, DOI:10.3970/cmes.2008.038.149
Abstract A novel meshfree poly-cell Galerkin method is developed for problems of elasticity and fracture. To improve accuracy, a poly-cell support is proposed to ensure the alignment of shape function support and the integration domain. By orthonormalizing basis functions, the improved moving least-square is formulated soundly, in which frequent matrix inversions are avoided. The Nitsche's method is introduced to treat the essential boundary conditions. It is found that computed solutions are more accurate than those obtained using the circle support used in standard MLS. Furthermore, numerical results present the superconvergent property, compared with the theoretical values More >

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Richardson Extrapolation Method for Singularly Perturbed Coupled System of Convection-Diffusion Boundary-Value Problems
Briti Sundar Deb¹, Srinivasan Natesan²
CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 179-200, 2008, DOI:10.3970/cmes.2008.038.179
Abstract This paper presents an almost second--order uniformly convergent Richardson extrapolation method for convection- dominated coupled system of boundary value problems. First, we solve the system by using the classical finite difference scheme on the layer resolving Shishkin mesh, and then we construct the Richardson approximation solution using the solutions obtained on N and 2N mesh intervals. Second-order parameter--uniform error estimate is derived. The proposed method is applied to a test example for verification of the theoretical results for the case ε ≤ N⁻¹. More >

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