Efficient computation of the Green's function and its derivatives for three-dimensional anisotropic elasticity in BEM analysis

Y. C. Shiah, C. L. Tan, C. Y. Wang

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

An alternative scheme to compute the Green's function and its derivatives for three dimensional generally anisotropic elastic solids is presented in this paper. These items are essential in the formulation of the boundary element method (BEM); their evaluation has remained a subject of interest because of the mathematical complexity. The Green's function considered here is the one introduced by Ting and Lee [Q. J. Mech. Appl. Math. 1997; 50: 407-26] which is of real-variable, explicit form expressed in terms of Stroh's eigenvalues. It has received attention in BEM only quite recently. By taking advantage of the periodic nature of the spherical angles when it is expressed in the spherical coordinate system, it is proposed that this Green's function be represented by a double Fourier series. The Fourier coefficients are determined numerically only once for a given anisotropic material; this is independent of the number of field points in the BEM analysis. Derivatives of the Green's function can be performed by direct spatial differentiation of the Fourier series. The resulting formulations are more concise and simpler than those derived analytically in closed form in previous studies. Numerical examples are presented to demonstrate the veracity and superior efficiency of the scheme, particularly when the number of field points is very large, as is typically the case when analyzing practical three dimensional engineering problems.

Original languageEnglish
Pages (from-to)1746-1755
Number of pages10
JournalEngineering Analysis with Boundary Elements
Volume36
Issue number12
DOIs
Publication statusPublished - 2012 Dec 1

All Science Journal Classification (ASJC) codes

  • Analysis
  • Engineering(all)
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Efficient computation of the Green's function and its derivatives for three-dimensional anisotropic elasticity in BEM analysis'. Together they form a unique fingerprint.

Cite this