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 `grading term' in this Green's function, originally deduced by Martin et al., 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