Y.C. Shiah¹, C. L. Tan², R.F. Lee¹

CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.2, pp. 167-198, 2010, DOI:10.3970/cmes.2010.069.167

Abstract In this paper, fully explicit, algebraic expressions are derived for the first and second derivatives of the Green's function for the displacements in a three dimensional anisotropic, linear elastic body. These quantities are required in the direct formulation of the boundary element method (BEM) for determining the stresses at internal points in the body. To the authors' knowledge, similar quantities have never previously been presented in the literature because of their mathematical complexity. Although the BEM is a boundary solution numerical technique, solutions for the displacements and stresses at internal points are sometimes required for More >

H.B. Chen¹, Masa. Tanaka²

CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.1, pp. 19-42, 2010, DOI:10.3970/cmes.2010.069.019

Abstract Highly accurate calculation of derivative values to the field variable is a key issue in numerical analysis of engineering problems. The boundary integral equations (BIEs) of potential second derivatives are of third order singularities and obviously the direct calculation of these high order singular integrals is rather cumbersome. The idea of the present paper is to use an indirect algorithm which is based on the regularized BIE formulations of the potential second derivatives, following the work of the present first author and his coworkers. The regularized formulations, numerical strategies and example tests are given for More >

Hua Zou¹, Hua Li^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.67, No.1, pp. 55-78, 2010, DOI:10.3970/cmes.2010.067.055

Abstract A novel meshless technique termed the Random Integral Quadrature (RIQ) method is developed in this paper for solving the generalized integral equations. By the RIQ method, the governing equations in the integral form are discretized directly with the field nodes distributed randomly or uniformly, which is achieved by discretizing the integral governing equations with the generalized integral quadrature (GIQ) technique over a set of background virtual nodes, and then interpolating the function values at the virtual nodes over a set of field nodes with Local Kriging method, where the field nodes are distributed either randomly… More >

V. Sladek¹, J. Sladek¹, Ch. Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.3, pp. 243-264, 2010, DOI:10.3970/cmes.2010.063.243

Abstract The paper deals with diminishing the prolongation of the computational time due to procedural evaluation of the shape functions and their derivatives in weak formulations implemented with meshless approximations. The proposed numerical techniques are applied to problems of stationary heat conduction in functionally graded media. Besides the investigation of the computational efficiency also the accuracy and convergence study are performed in numerical tests. More >

Yue-Ting Zhou¹, Xing Li², De-Hao Yu³, Kang Yong Lee^1,4

CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.2, pp. 163-190, 2010, DOI:10.3970/cmes.2010.063.163

Abstract In this paper, a coupled crack/contact model is established for the composite material with arbitrary periodic cracks indented by periodic punches. The contact of crack faces is considered. Frictional forces are modeled to arise between the punch foundation and the composite material boundary. Kolosov-Muskhelisvili complex potentials with Hilbert kernels are constructed, which satisfy the continuity conditions of stress and displacement along the interface identically. The considered problem is reduced to a system of singular integral equations of first and second kind with Hilbert kernels. Bounded functions are defined so that singular integral equations of Hilbert More >

Roman Chapko¹, B. Tomas Johansson², Oleh Sobeyko¹

CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.1, pp. 57-76, 2010, DOI:10.3970/cmes.2010.062.057

Abstract We propose an iterative procedure for the inverse problem of determining the displacement vector on the boundary of a bounded planar inclusion given the displacement and stress fields on an infinite (planar) line-segment. At each iteration step mixed boundary value problems in an elastostatic half-plane containing the bounded inclusion are solved. For efficient numerical implementation of the procedure these mixed problems are reduced to integral equations over the bounded inclusion. Well-posedness and numerical solution of these boundary integral equations are presented, and a proof of convergence of the procedure for the inverse problem to the More >

E. J. Sellountos¹, A. Sequeira¹, D. Polyzos²

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.2, pp. 109-136, 2010, DOI:10.3970/cmes.2010.057.109

Abstract A new Local Boundary Integral Equation (LBIE) method is proposed for the solution of plane elastostatic problems. Non-uniformly distributed points taken from a Finite Element Method (FEM) mesh cover the analyzed domain and form background cells with more than four points each. The FEM mesh determines the position of the points without imposing any connectivity requirement. The key-point of the proposed methodology is that the support domain of each point is divided into parts according to the background cells. An efficient Radial Basis Functions (RBF) interpolation scheme is exploited for the representation of displacements in More >

B. Chandrasekhar¹

CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.3, pp. 211-230, 2010, DOI:10.3970/cmes.2010.056.211

Abstract In this work, various basis functions used in the Method of Moments or Boundary Element (MoM/BEM) solution of acoustic scattering problems are compared with each other for their performance. Single layer formulation of the rigid bodies is considered in comparison of the solutions. Geometry of a scatterer is descritized using triangular patch modeling and basis functions are defined on triangular patches, edges and nodes for three different solutions. Far field scattering cross sections for different frequencies of incident acoustic wave are compared with the closed form solutions. Also, the errors of the solutions using these More >

Sheng-Hu Ding^1,2, Xing Li², Yue-Ting Zhou^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.1, pp. 43-84, 2010, DOI:10.3970/cmes.2010.056.043

Abstract In this paper, the crack-tip fields in bonded functionally graded finite strips are studied. Different layers may have different nonhomogeneity properties in the structure. A bi-parameter exponential function was introduced to simulate the continuous variation of material properties. The problem was reduced as a system of Cauchy singular integral equations of the first kind by Laplace and Fourier integral transforms. Various internal cracks and edge crack and crack crossing the interface configurations are investigated, respectively. The asymptotic stress field near the tip of a crack crossing the interface is examined and it is shown that, More >

M. A. Kelmanson¹ and M. C. Tenwick¹

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 191-210, 2010, DOI:10.3970/cmes.2010.055.191

Abstract A method is presented for improving the accuracy of the widely used Gauss-Legendre Nyström method for determining approximate solutions of Fredholm integral equations of the second kind on finite intervals. The authors' recent continuous-kernel approach is generalised in order to accommodate kernels that are either singular or of limited continuous differentiability at a finite number of points within the interval of integration. This is achieved by developing a Gauss-Jacobi Nyström method that moreover includes a mean-value estimate of the truncation error of the Hermite interpolation on which the quadrature rule is based, making it particularly More >