@Article{cmes.2007.022.151,
AUTHOR = {R.  Criado, J.E.  Ortiz, V. Mantič, L.J.  Gray, F.  París},
TITLE = {Boundary Element Analysis of Three-Dimensional Exponentially Graded Isotropic Elastic Solids},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {22},
YEAR = {2007},
NUMBER = {2},
PAGES = {151--164},
URL = {http://www.techscience.com/CMES/v22n2/25055},
ISSN = {1526-1506},
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, <i>U<sub>jl</sub></i>, was deduced by Martin et al. (<i>Proc. R. Soc. Lond. A</i>, <b>458</b>, pp. 1931--1947, 2002). This expression was recently corrected and implemented in a Galerkin indirect 3D BEM code by Criado et al. (<i>Int. J. Numer. Meth. Engng.</i>, 2008). Starting from this expression of <i>U<sub>jl</sub></i>, a new expression for the fundamental solution in tractions <i>T<sub>jl</sub></i> has been deduced in the present work. These quite complex expressions of the integral kernels <i>U<sub>jl</sub></i> and <i>T<sub>jl</sub></i> 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 <i>T<sub>jl</sub></i> is correct. Excellent accuracy is obtained with very coarse boundary element meshes, even for a relatively high grading of elastic properties considered.},
DOI = {10.3970/cmes.2007.022.151}
}