Y.C. Shiah¹, C. L. Tan²

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.2, pp. 95-108, 2011, DOI:10.3970/cmes.2011.078.095

Abstract By differentiating the Green function of Ting and Lee (1997) for 3D general anisotropic elastotatics in a spherical coordinate system as an intermediate step, and then using the chain rule, derivatives of up to the second order of this fundamental solution are obtained in exact, explicit, algebraic forms. No tensors of order higher than two are present in these derivatives, thereby allowing these quantities to be numerically evaluated quite expeditiously. These derivatives are required for the computation of the internal point displacements and stresses via Somigliana's identity in BEM analysis. Some examples are presented to More >

A. Aimi¹, M. Diligenti¹, S. Panizzi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.2, pp. 185-220, 2010, DOI:10.3970/cmes.2010.058.185

Abstract In this paper we consider 2D wave propagation Neumann exterior problems reformulated in terms of a hypersingular boundary integral equation with retarded potential. Starting from a natural energy identity satisfied by the solution of the differential problem, the related integral equation is set in a suitable space-time weak form. Then, a theoretical analysis of the introduced formulation is proposed, pointing out the novelties with respect to existing literature results. At last, various numerical simulations will be presented and discussed, showing accuracy and stability of the space-time Galerkin boundary element method applied to the energetic weak More >

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 >

R. Criado¹, J.E. Ortiz¹, V. Mantič¹, L.J. Gray^1,2, F. París¹

CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.2, pp. 151-164, 2007, DOI:10.3970/cmes.2007.022.151

Abstract A numerical implementation of the Somigliana identity in displacements for the solution of 3D elastic problems in exponentially graded isotropic solids is presented. An expression for the fundamental solution in displacements, U_jl, was deduced by Martin et al. (Proc. R. Soc. Lond. A, 458, pp. 1931--1947, 2002). This expression was recently corrected and implemented in a Galerkin indirect 3D BEM code by Criado et al. (Int. J. Numer. Meth. Engng., 2008). Starting from this expression of U_jl, a new expression for the fundamental solution in tractions T_jl has been deduced in the present work. These quite complex expressions of More >

Youssef F. Rashed¹

CMC-Computers, Materials & Continua, Vol.1, No.4, pp. 319-326, 2004, DOI:10.3970/cmc.2004.001.319

Abstract The present paper develops a new technique for treatment of self-weight for building slabs in the boundary element method (BEM). Due to the use of BEM in the analysis, all defined variables are presented on the slab boundary (mesh is defined only along the slab boundary). Self-weight, however, is usually defined over slab domain, hence domain discretisation is required, which spoils the main advantage of the BEM. In this paper a new method is presented to transform self-weight domain integrals to the boundary for such slabs. The proposed method is based on using the so-called More >