C. F. Loeffler¹, R. G. Peixoto²

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.4, pp. 253-276, 2013, DOI:10.3970/cmes.2013.093.253

Abstract Here is presented a formal deduction for the Dual Reciprocity hypersingular boundary integral equation for application to two dimensional potential problems. The theoretical and numerical derivations are presented in detail, and some simple test problems are included to verify the accuracy of the proposed formulation. Due to its simplicity, Poisson’s Equation is used as a basis for the mathematical formulations and operational procedures related to the body force term, but the methodology can easily be extended to other more elaborate classes of potential problems. Poles are inserted internally to improve the interpolation within the domain, resulting in a hybrid singular… More >

Wen-Ping Wu^1,2, Zong-Zhuan Yao³

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.4, pp. 235-252, 2013, DOI:10.3970/cmes.2013.093.235

Abstract The internal microstructure evolution and atomic stress distribution around the crack tip of a pre-cracked single crystal nickel with unequal sample sizes are studied by molecular dynamics (MD) simulation. The simulated results indicate that the crack propagation dynamics and stress distributions around the crack tip are strongly dependent on the microstructure evolution caused by the change of sample size. Unequal sample sizes induce various atomic configurations around the crack tip during the crack propagation. When atomic configuration is invariable around the crack tip, the crack grows rapidly along the crack path, the stress concentration occurs at the crack tip of… More >

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 reaching the analytical solution in… More >

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 the approximate temperature and heat… More >

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 >

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 crack tip where the dislocation… More >

Wen-Hwa Chen^2,3, Ming-Hsiao Lee⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.2, pp. 149-166, 2013, DOI:10.3970/cmes.2013.093.149

Abstract A novel meshless analysis procedure is established for practical implementation in dealing with three-dimensional structures with complicated geometry. By this procedure, to describe the surface of structure, the Stereo-lithography (STL) geometry technique is first adopted. Nodes are then generated and paved uniformly in the space over the entire structure analyzed. To decide the node distribution inside the structure, a geometry-related treatment scheme with relevant checking mechanisms is developed. Besides, a simple and direct spatial integration scheme is also proposed. By this integration scheme, integration points are evenly distributed in the structure and can be adjusted easily to meet the required… More >

K.-C. Wu², S.-M. Huang², S.-H. Chen³

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.2, pp. 133-148, 2013, DOI:10.3970/cmes.2013.093.133

Abstract An analysis is presented for an array of collinear cracks subject to a uniform tensile stress wave in an isotropic material. An integral equation for the problem is established by modeling the cracks as distributions of dislocations. The integral equation is solved numerically in the Laplace transform domain first and the solution is then inverted to the time domain to calculate the dynamic stress intensity factors. Numerical examples of one, two, or three collinear cracks are given. The results of one or two cracks are checked to agree closely with the existing results. More >

J.H. Lv¹, Y. Miao^1,2, W.H. Gong¹, H.P. Zhu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.2, pp. 113-131, 2013, DOI:10.3970/cmes.2013.093.113

Abstract Accurate numerical evaluation of the nearly singular boundary integrals is a major concerned issue in the implementation of boundary element method (BEM). In this paper, a general distance function independent on the nearly singular point is proposed. Combined with an iteration process, the position of the nearly singular point can be obtained more easily. Then, an extended form of the sinh transformation using the general distance function, which automatically takes into account the intrinsic coordinate of the nearly singular point and the minimum distance from source point to the element in the intrinsic parameter plane, is developed to deal with… More >

P. K. Sahu¹, S. Saha Ray^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.2, pp. 91-112, 2013, DOI:10.3970/cmes.2013.093.091

Abstract In this paper, nonlinear integral equations have been solved numerically by using B-spline wavelet method and Variational Iteration Method (VIM). Compactly supported semi-orthogonal linear B-spline scaling and wavelet functions together with their dual functions are applied to approximate the solutions of nonlinear Fredholm integral equations of second kind. Comparisons are made between the variational Iteration Method (VIM) and linear B-spline wavelet method. Several examples are presented to compare the accuracy of linear B-spline wavelet method and Variational Iteration Method (VIM) with their exact solutions. More >