On simple formulations of weakly-singular traction & displacement BIE, and their solutions through Petrov-Galerkin approaches

Z. D. Han, S. N. Atluri

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58 Scopus citations

Abstract

Using the directly derived non-hyper singular integral equations for displacement gradients [as in Okada, Rajiyah, and Atluri (1989a)], simple and straight-forward derivations of weakly singular traction BIE's for solids undergoing small deformations are presented. A large number of "intrinsic properties" of the fundamental solutions in elasticity are developed, and are used in rendering the tBIE and dBIE to be only weakly-singular, in a very simple manner. The solutions of the weakly singular tBIE and dBIE through either global Petrov-Galerkin type "boundary element methods", or, alternatively, through the meshless local Petrov-Galerkin (MLPG) methods, are discussed. As special cases, the Galerkin type methods, which lead to symmetric systems of equations, are also discussed.

Original languageEnglish
Pages (from-to)5-20
Number of pages16
JournalCMES - Computer Modeling in Engineering and Sciences
Volume4
Issue number1
StatePublished - 2003

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