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Internal Point Solutions for Displacements and Stresses in 3D Anisotropic Elastic Solids Using the Boundary Element Method

Y.C. Shiah1, C. L. Tan2, R.F. Lee1
Dept. of Aerospace and Systems Engineering, Feng Chia University, Taichung, Taiwan, R.O.C.
Dept. of Mechanical & Aerospace Engineering, Carleton University, Ottawa, Canada K1S 5B6

Computer Modeling in Engineering & Sciences 2010, 69(2), 167-198. https://doi.org/10.3970/cmes.2010.069.167

Abstract

In this paper, fully explicit, algebraic expressions are derived for the first and second derivatives of the Green's function for the displacements in a three dimensional anisotropic, linear elastic body. These quantities are required in the direct formulation of the boundary element method (BEM) for determining the stresses at internal points in the body. To the authors' knowledge, similar quantities have never previously been presented in the literature because of their mathematical complexity. Although the BEM is a boundary solution numerical technique, solutions for the displacements and stresses at internal points are sometimes required for some engineering applications. To this end, the availability of the derivatives of the fundamental solution in closed, algebraic form enables their implementation into an existing BEM code in a relatively straightforward manner. Some examples are presented to demonstrate the veracity of these expressions and their successful implementation for determining interior point solutions in 3D general anisotropic elastostatics in BEM.

Keywords

Boundary element method, Green's functions, boundary integral equations, Somigliana's identity, anisotropic elasticity, Stroh's eigenvalues.

Cite This Article

Shiah, Y., Tan, C. L., Lee, R. (2010). Internal Point Solutions for Displacements and Stresses in 3D Anisotropic Elastic Solids Using the Boundary Element Method. CMES-Computer Modeling in Engineering & Sciences, 69(2), 167–198.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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