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Title: 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.

Authors:
 [1];  [1];  [2];  [2]
  1. ORNL
  2. University of Seville
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
979071
DOE Contract Number:  
DE-AC05-00OR22725
Resource Type:
Journal Article
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Journal Volume: 74; Journal Issue: 10; Journal ID: ISSN 0029-5981
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; APPROXIMATIONS; ELASTICITY; EVALUATION; IMPLEMENTATION; SOLIDS

Citation Formats

Criado Portero, Rafael M, Gray, Leonard J, Mantic, Vladislav, and Paris, Federico. Green's function evaluation for three-dimensional exponentially graded elasticity. United States: N. p., 2008. Web. doi:10.1002/nme.2223.
Criado Portero, Rafael M, Gray, Leonard J, Mantic, Vladislav, & Paris, Federico. Green's function evaluation for three-dimensional exponentially graded elasticity. United States. https://doi.org/10.1002/nme.2223
Criado Portero, Rafael M, Gray, Leonard J, Mantic, Vladislav, and Paris, Federico. 2008. "Green's function evaluation for three-dimensional exponentially graded elasticity". United States. https://doi.org/10.1002/nme.2223.
@article{osti_979071,
title = {Green's function evaluation for three-dimensional exponentially graded elasticity},
author = {Criado Portero, Rafael M and Gray, Leonard J and Mantic, Vladislav and Paris, Federico},
abstractNote = {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.},
doi = {10.1002/nme.2223},
url = {https://www.osti.gov/biblio/979071}, journal = {International Journal for Numerical Methods in Engineering},
issn = {0029-5981},
number = 10,
volume = 74,
place = {United States},
year = {Tue Jan 01 00:00:00 EST 2008},
month = {Tue Jan 01 00:00:00 EST 2008}
}