SUMMARYThe numerical implementation of Green's function for an isotropic exponentially graded three-dimensional elastic solid is reported. The formulas for the non-singular 'grading term' in this Green's function, originally deduced by Martin et al. (Proc. R. Soc. Lond. Ser. A 2002; 458:1931-1947, are quite complicated, and a small error in one of the formulas is corrected. The evaluation of the fundamental solution is tested by employing an indirect boundary integral formulation using a Galerkin approximation to solve several problems having analytic solutions. The numerical results indicate that Green's function formulas, and their evaluation, are correct.
A parallel domain decomposition boundary integral algorithm for three-dimensional exponentially graded elasticity has been developed. As this subdomain algorithm allows the grading direction to vary in the structure, geometries arising from practical functionally graded material applications can be handled. Moreover, the boundary integral algorithm scales well with the number of processors, also helping to alleviate the high computational cost of evaluating the Green’s functions. For axisymmetric plane strain states in a radially graded material, the numerical results for cylindrical geometries are in excellent agreement with the analytical solution deduced herein.
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