CMES-Vol. 93, No. 3, 2013

Open Access

ARTICLE

Solutions of a Crack Interacting with Tri-Material Composite in Plane Elasticity
C.K. Chao¹, A. Wikarta²
CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.3, pp. 167-186, 2013, DOI:10.3970/cmes.2013.093.167
Abstract In this paper a crack interacting with tri-material composite under a remote uniform tensile load is solved in plane elasticity. An edge dislocation distribution along the prospective site of the crack together with the principle of superposition is used to model a crack. The resulting singular integral equation with logarithmic singular kernels for a line crack is then established. The singular integral equation is solved numerically by modeling a crack in place of several segments. Linear interpolation formulae with undetermined coefficients are applied to approximate the dislocation distribution along the elements, except at vicinity of More >

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ARTICLE

The Second Kind Chebyshev Wavelet Method for Fractional Differential Equations with Variable Coefficients
Baofeng Li¹
CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.3, pp. 187-202, 2013, DOI:10.3970/cmes.2013.093.187
Abstract In this article, the second kind Chebyshev wavelet method is presented for solving a class of multi-order fractional differential equations (FDEs) with variable coefficients. We first construct the second kind Chebyshev wavelet, prove its convergence and then derive the operational matrix of fractional integration of the second kind Chebyshev wavelet. The operational matrix of fractional integration is utilized to reduce the fractional differential equations to a system of algebraic equations. In addition, illustrative examples are presented to demonstrate the efficiency and accuracy of the proposed method. More >

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Cauchy Problem for the Laplace Equation in 2D and 3D Doubly Connected Domains
Ji-Chuan Liu¹, Quan-Guo Zhang²
CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.3, pp. 203-220, 2013, DOI:10.3970/cmes.2013.093.203
Abstract In this paper, we propose an algorithm to solve a Cauchy problem of the Laplace equation in doubly connected domains for 2D and 3D cases in which the Cauchy data are given on the outer boundary. We want to seek a solution in the form of the single-layer potential and discrete it by parametrization to yield an ill-conditioned system of algebraic equations. Then we apply the Tikhonov regularization method to solve this ill-posed problem and obtain a stable numerical solution. Based on the regularization parameter chosen suitably by GCV criterion, the proposed method can get More >

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ARTICLE

Numerical Analysis on Dual Holes Interactions
C. K. Chen¹
CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.3, pp. 221-234, 2013, DOI:10.3970/cmes.2013.093.221
Abstract By extending Bückner’s superposition principle and alternating iteration method, this presentation studies the dual holes interactions. A newly developed numerical scheme is embedded in the conventional Gauss-Legendre quadrature routine for evaluating the boundary integral holding stress singularities. This developed scheme can avoid numerical singularity and facilitate the achieved stress field to be exact as that of analytical solution; however the chosen Gaussian integration points must enter a large quantity. This presentation uses an infinite plate with a centered hole strained by remote axial loading as a testing example, and the numerical results are capable of More >

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