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 Uj`, 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. for Numerical Methods in Engineering, 2006). Starting from this expression of Uj`, a new expression for the fundamental solution in tractions Tj` has been deduced in the present work. These quite complex expressions of the integral kernels Uj` and Tj` 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 Tj` 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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