Analysis of Two-Dimensional Steady-State Heat Conduction in Anisotropic Solids by Boundary Element Method Using Analog Equation Method and Green's Theorem

This paper is concerned with the application of the boundary element method (BEM) with the analog equation method (AEM), proposed by Katsikadelis and Nerantzaki, and Green's theorem to analyze steady-state heat conduction in anisotropic solids. In this study, the linear differential operator (the Laplacian) of steady-state heat conduction in isotropic solids is extracted from the governing differential equation. The integral equation formulated employs the fundamental solution of the Laplace equation for isotropic solids, and therefore, from the anisotropic part of the governing differential equation, a domain integral appears in the boundary integral equation. This domain integral is transformed into boundary integrals using Green's theorem with a polynomial function. The mathematical formulation of this approach for two-dimensional problems is presented in detail. The proposed solution is applied to two typical examples, and the validity and other numerical properties of the proposed BEM are demonstrated in the discussion of the results obtained.