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

R. Criado1, J.E. Ortiz1, V. Mantič1, L.J. Gray1,2, F. París1
School of Engineering, University of Seville, Camino delos Descubrimientos s/n, Sevilla, E-41092, Spain
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.


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, Ujl, 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 Ujl, a new expression for the fundamental solution in tractions Tjl has been deduced in the present work. These quite complex expressions of the integral kernels Ujl and Tjl 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 Tjl is correct. Excellent accuracy is obtained with very coarse boundary element meshes, even for a relatively high grading of elastic properties considered.


functionally graded materials, boundary element method, three-dimensional elasticity, Somigliana identity, fundamental solution in tractions.

Cite This Article

Criado, R., Ortiz, J., Mantič, V., Gray, L., París, F. (2007). Boundary Element Analysis of Three-Dimensional Exponentially Graded Isotropic Elastic Solids. CMES-Computer Modeling in Engineering & Sciences, 22(2), 151–164.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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