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Higher-Order Green's Function Derivatives and BEM Evaluation of Stresses at Interior Points in a 3D Generally Anisotropic Solid

Y.C. Shiah1, C. L. Tan2

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 2011, 78(2), 95-108. https://doi.org/10.3970/cmes.2011.078.095

Abstract

By differentiating the Green function of Ting and Lee (1997) for 3D general anisotropic elastotatics in a spherical coordinate system as an intermediate step, and then using the chain rule, derivatives of up to the second order of this fundamental solution are obtained in exact, explicit, algebraic forms. No tensors of order higher than two are present in these derivatives, thereby allowing these quantities to be numerically evaluated quite expeditiously. These derivatives are required for the computation of the internal point displacements and stresses via Somigliana's identity in BEM analysis. Some examples are presented to demonstrate their successful implementation to this end, in which the numerical results are compared with corresponding values obtained using the finite element method (FEM). An assessment of the relative efficiency of the BEM analysis when using the present exact form of the derivatives versus another previous exact form is also presented.

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Cite This Article

Shiah, Y., Tan, C. L. (2011). Higher-Order Green's Function Derivatives and BEM Evaluation of Stresses at Interior Points in a 3D Generally Anisotropic Solid. CMES-Computer Modeling in Engineering & Sciences, 78(2), 95–108.



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