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

Z. D. Han1, S. N. Atluri1
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.

Cite This Article

Han, Z. D., Atluri, S. N. (2003). On Simple Formulations of Weakly-Singular Traction & Displacement BIE, and Their Solutions through Petrov-Galerkin Approaches. CMES-Computer Modeling in Engineering & Sciences, 4(1), 5–20.



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