Open Access

ARTICLE

The Boundary Integral Equation for 3D General Anisotropic Thermoelasticity

by Y.C. Shiah¹, C.L. Tan²

1 Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan 701, Taiwan, R.O.C.
2 Department of Mechanical & Aerospace Engineering, Carleton University, Ottawa, Canada K1S5B6.
3 Corresponding author. E-mail: choonlai.tan@carleton.ca

Computer Modeling in Engineering & Sciences 2014, 102(6), 425-447. https://doi.org/10.3970/cmes.2014.102.425

Abstract

Green’s functions, or fundamental solutions, are necessary items in the formulation of the boundary integral equation (BIE), the analytical basis of the boundary element method (BEM). In the formulation of the BEM for 3D general anisotropic elasticity, considerable attention has been devoted to developing efficient algorithms for computing these quantities over the years. The mathematical complexity of this Green’s function has also posed an obstacle in the development of this numerical method to treat problems of 3D anisotropic thermoelasticity. This is because thermal effects manifest themselves as an additional domain integral in the integral equation; this has implications for the numerical modeling in BEM. Difficulties in deriving a true BIE arise, unless some simple representations of the thermal effects are used, such as in the dual reciprocity approach. These approximation schemes, however, have some serious limitations. An integral transformation method to obtain an exact BIE has been successfully employed, but only for isotropy and two-dimensional (2D) general anisotropy. The extension of this scheme to three-dimensional (3D) general anisotropy has remained a very serious challenge. This paper reports on the progress towards this end. By following the same steps as for 2D general anisotropy, and using a double-Fourier series representation of the Green’s function first proposed by the authors recently, a true BIE is derived for 3D general anisotropic thermoelasticity. Some numerical results are presented to demonstrate the success of this derivation.

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