Analysis of Two-Dimensional Nonlinear Transient Heat Conduction in Anisotropic Solids by Boundary Element Method Using Dual Reciprocity Method

概要

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This paper is concerned with an application of the boundary element method (BEM) using the dual reciprocity method (DRM) to analyze nonlinear transient heat conduction in anisotropic solids. In this study, because the fundamental solution of this problem has not previously been obtained, the concept (the analog equation method) proposed by Katsikadelis and Nerantzaki is applied. A standard linear partial differential operator, in which the fundamental solution can be obtained, can be extracted from a nonlinear partial differential equation. One can consider the remainder as a body force and solve the equation using DRM. Mathematical formulations of this approach for two-dimensional problems are presented in detail. Two schemes are discussed in this paper: The “isotropic” scheme, in which the operator of steady-state heat conduction in isotropic solids is extracted, and the “anisotropic” scheme, where the operator of the steady-state heat conduction in anisotropic solids is extracted. The proposed solution procedure is applied to a couple of typical examples, and the validity and other numerical properties of the proposed BEM are demonstrated through discussions of the results obtained.