Open Access

ARTICLE

Evaluation of Explicit-form Fundamental Solutions for Displacements and Stresses in 3D Anisotropic Elastic Solids

by Y. C. Shiah¹, C. L. Tan², V.G. Lee³

1 Dept. of Aerospace and Systems Engineering, Feng Chia University, Taichung, Taiwan, R.O.C.
2 Dept. of Mechanical & Aerospace Engineering, Carleton University, Ottawa, Canada K1S 5B6.
3 Dept. of Civil Engineering, National Chi Nan University, Nantou, Taiwan, R.O.C.

Computer Modeling in Engineering & Sciences 2008, 34(3), 205-226. https://doi.org/10.3970/cmes.2008.034.205

Abstract

The main impediment to the development of efficient algorithms for the stress analysis of 3D generally anisotropic elastic solids using the boundary element method (BEM) and the local boundary integral equation (LBIE) meshless method over the years is the complexity of the fundamental solutions and the computational burden to evaluate them. The ability to analytically simplify and reduce them into as explicit a form as possible so that they can be directly computed will offer significant cost savings. In addition, they facilitate easy implementation using existing numerical algorithms with the above-mentioned methods that have been developed for isotropy. In this paper, the explicit, real-variable forms of the fundamental solutions for the displacements and stresses are presented as algebraic expressions in terms of Stroh's eigenvalues. Although derived by one of the present authors some years ago, they have never been utilized in BEM or LBIE methods and their numerical evaluations have never been assessed. The veracity of these expressions and the direct manner with which numerical values can be obtained are demonstrated by some examples here.

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Keywords

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