Direct volume-to-surface integral transformation for 2D BEM analysis of anisotropic thermoelasticity

As has been well documented for the boundary element method (BEM), a volume integral is present in the integral equation for thermoelastic analysis. Any attempt to directly integrate the integral shall inevitably involve internal discretization that will destroy the BEM's distinctive notion as a true boundary solution technique. Among the schemes to overcome this difficulty, the exact transformation approach is the most elegant since neither further approximation nor internal treatments are involved. Such transformation for 2D anisotropic thermoelasticity has been achieved by Shiah and Tan (1999) with the aid of domain mapping. This paper revisits this problem and presents a modified transformation for 2D anisotropic thermoelasticity, where no domain distortion is involved. Being defined in the original Cartesian coordinate system, the volume integral is analytically transformed to the boundary using the Stroh formalism. This transformation is favorable especially when the corresponding anisotropic field is directly calculated without resorting to the domain mapping technique. In the end, numerical examples are provided to show the validity of such a transformation.