Open Access

ARTICLE

On Simple Formulations of Weakly-Singular Traction & Displacement BIE, and Their Solutions through Petrov-Galerkin Approaches

Z. D. Han¹, S. N. Atluri¹

1 Center for Aerospace Research & Education, University of California, Irvine, 5251 California Avenue, Suite 140, Irvine, CA 92612, USA

Computer Modeling in Engineering & Sciences 2003, 4(1), 5-20. https://doi.org/10.3970/cmes.2003.004.005

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.

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