Green’s function evaluation for three-dimensional exponentially graded elasticity

Abstract

The numerical implementation of the Green's function for an isotropic exponentially graded three dimensional elastic solid is reported. The formulas for the nonsingular {lq}grading term{rq} in this Green's function, originally deduced by Martin et al., emph{Proc. R. Soc. Lond. A, 458, 1931-1947, 2000}, are quite complicated, and a small error in one of the formulas is corrected. The evaluation of the fundamental solution is tested by employing indirect boundary integral formulation using a Galerkin approximation to solve several problems having analytic solutions. The numerical results indicate that the Green's function formulas, and their evaluation, are correct.