Open Access

ARTICLE

BEM Analysis of 3D Heat Conductionin 3D Thin Anisotropic Media

Y.C. Shiah¹, Y.M. Lee², Chi-Chang Wang²

1 Corresponding author, Email:ycshiah@mail.ncku.edu.tw; Fax:+886-424510862; Tel:+88624517250 ext.3956.
Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan 701, Taiwan.
2 Ph. D. program in Mechanical and Aeronautical Engineering. Feng Chia University, Taichung 407, Taiwan.

Computers, Materials & Continua 2013, 33(3), 229-255. https://doi.org/10.3970/cmc.2013.033.229

Abstract

In this paper, the boundary integrals for treating 3D field problems are fully regularized for planar elements by the technique of integration by parts (IBP). As has been well documented in open literatures, these integrals appear to be strongly singular and hyper-singular for the associated fundamental solutions. In the past, the IBP approach has only been applied to regularize the integrals for 2D problems. The present work shows that the IBP can also be further extended to treat 3D problems, where two variables of the local coordinates are involved. The presented formulations are fully explicit and also, most importantly, very straightforward for implementation in program codes. To demonstrate their validity and our implementation, a few example cases of 3D anisotropic heat conduction are investigated by the boundary element method and the calculated results are verified using analyses by ANSYS.

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Keywords

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