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Green's function evaluation for three‐dimensional exponentially graded elasticity
Author(s) -
Criado R.,
Gray L. J.,
Mantič V.,
París F.
Publication year - 2007
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2223
Subject(s) - mathematics , isotropy , mathematical analysis , galerkin method , elasticity (physics) , exponential growth , green's function , boundary value problem , function (biology) , finite element method , physics , quantum mechanics , evolutionary biology , biology , thermodynamics
The 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 2000; 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. Copyright © 2007 John Wiley & Sons, Ltd.