TY  - EJOU
AU  - Criado, R.  
AU  - Ortiz, J.E.  
AU  - Mantič, V. 
AU  - Gray, L.J.  
AU  - París, F.  

TI  - Boundary Element Analysis of Three-Dimensional Exponentially Graded Isotropic Elastic Solids
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2007
VL  - 22
IS  - 2
SN  - 1526-1506

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

DO  - 10.3970/cmes.2007.022.151