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ARTICLE

Boundary Element Analysis of Three-Dimensional Exponentially Graded Isotropic Elastic Solids

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

1 School of Engineering, University of Seville, Camino delos Descubrimientos s/n, Sevilla, E-41092, Spain
2 Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6367, USA

Computer Modeling in Engineering & Sciences 2007, 22(2), 151-164. https://doi.org/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 the integral kernels U_jl and T_jl have been implemented in a collocational direct 3D BEM code. The numerical results obtained for 3D problems with known analytic solutions verify that the new expression for T_jl is correct. Excellent accuracy is obtained with very coarse boundary element meshes, even for a relatively high grading of elastic properties considered.

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