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An Exact Boundary Integral Equation Formulation for BEM Thermoelastic Analysis of Transversely Anisotropic Solids

Y. C. Shiah1, C. L. Tan2

1 Dept. of Aerospace and Systems Engineering, FengChia University, Taichung, Taiwan R.O.C.
2 Dept. of Mechanical & Aerospace Engineering, Carleton University, Ottawa, Canada K1S 5B6

Structural Longevity 2012, 8(2), 99-107. https://doi.org/10.3970/sl.2012.008.099

Abstract

In BEM analysis of generally anisotropic solids, the additional volume integral associated with thermal effects that appears in the direct formulation of the boundary integral equation (BIE) has hitherto been successfully transformed in an analytically exact fashion into surface ones only for two-dimensions (2D), and not for the three-dimensional (3D) case. This is due to the mathematical complexity of the Green’s function and its derivatives for the 3D solid. The presence of the domain integral destroys the distinctive feature of the boundary element method (BEM) as a truly boundary solution numerical analysis tool. As a precursor to treating this problem in 3D general anisotropy, the exact volume-to-surface integral transformation associated with thermal effects is successfully carried out in this study for the special case of 3D transverse isotropy and implemented in a BEM formulation. It follows a similar approach previously employed by the authors for the same task in 2D generally anisotropic thermoelastic BEM analysis. However, a numerical scheme needs to be introduced to evaluate some terms in the new surface integrals of the BIE. Two examples are presented to demonstrate the veracity of the analytical and numerical formulations implemented.

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Shiah, Y. C., Tan, C. L. (2012). An Exact Boundary Integral Equation Formulation for BEM Thermoelastic Analysis of Transversely Anisotropic Solids. Structural Longevity, 8(2), 99–107. https://doi.org/10.3970/sl.2012.008.099



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