CMES-Vol. 30, No. 2, 2008

Open Access

ARTICLE

Analysis of the interaction between two nanovoids using bipolar coordinates
Shuling Hu¹, Shengping Shen^1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.2, pp. 57-64, 2008, DOI:10.3970/cmes.2008.030.057
Abstract The effects of surface energy on the interaction between two voids of equal size are investigated. The problem is solved by series expansion in bipolar coordinates. The results show that the surface energy significantly affects the stress concentration around the holes as the size of the holes shrinks to nanometers, meanwhile the interaction between the holes also influences the stress distribution around the holes, which become evident as the holes close to each other. This problem is of great importance in engineering applications. More >

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ARTICLE

A Highly Accurate MCTM for Direct and Inverse Problems of Biharmonic Equation in Arbitrary Plane Domains
Chein-Shan Liu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.2, pp. 65-76, 2008, DOI:10.3970/cmes.2008.030.065
Abstract Trefftz method (TM) is one of widely used meshless numerical methods in elliptic type boundary value problems, of which the approximate solution is expressed as a linear combination of T-complete bases, and the unknown coefficients are determined from boundary conditions by solving a linear equations system. However, the accuracy of TM is severely limited by its ill-conditioning. This paper is a continuation of the work of Liu (2007a). The collocation TM is modified and applied to the direct and inverse problems of biharmonic equation in a simply connected plane domain. Due to its well-conditioning of More >

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ARTICLE

Thermal Analysis of Reissner-Mindlin Shallow Shells with FGM Properties by the MLPG
J. Sladek¹, V. Sladek¹, P. Solek², P.H. Wen³, S.N. Atluri⁴
CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.2, pp. 77-98, 2008, DOI:10.3970/cmes.2008.030.077
Abstract A meshless local Petrov-Galerkin (MLPG) method is applied to solve problems of Reissner-Mindlin shells under thermal loading. Both stationary and thermal shock loads are analyzed here. Functionally graded materials with a continuous variation of properties in the shell thickness direction are considered here. A weak formulation for the set of governing equations in the Reissner-Mindlin theory is transformed into local integral equations on local subdomains in the base plane of the shell by using a unit test function. Nodal points are randomly spread on the surface of the plate and each node is surrounded by More >

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The Method of Fundamental Solutions for Inverse Problems Associated with the Steady-State Heat Conduction in the Presence of Sources
Liviu Marin¹
CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.2, pp. 99-122, 2008, DOI:10.3970/cmes.2008.030.099
Abstract The application of the method of fundamental solutions (MFS) to inverse boundary value problems associated with the steady-state heat conduction in isotropic media in the presence of sources, i.e. the Poisson equation, is investigated in this paper. Based on the approach of Alves and Chen (2005), these problems are solved in two steps, namely by finding first an approximate particular solution of the Poisson equation and then the numerical solution of the resulting inverse boundary value problem for the Laplace equation. The resulting MFS discretised system of equations is ill-conditioned and hence it is solved More >

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