CMES-Vol. 93, No. 2, 2013

Open Access

ARTICLE

Numerical Approximate Solutions of Nonlinear Fredholm Integral Equations of Second Kind Using B-spline Wavelets and Variational Iteration Method
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 >

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The Sinh Transformation for Curved Elements Using the General Distance Function
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, More >

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Dynamic Stress Intensity Factors of Collinear Cracks under a Uniform Tensile Stress Wave
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 >

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A Novel Meshless Analysis Procedure for Three-dimensional Structural Problems with Complicated Geometry
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 More >

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