Analysis of the temperature field in anisotropic coating-structures by the boundary element method

摘要

The distance r between the source point and the field point is very short when the boundary element method is used to calculate the boundary quantities in the coating domain, which is very thin with respect to the substrate. The nearly singular integrals will occur during the process of numerical calculation of the boundary integral equations when the distance r is approaching to zero. The calculation difficulty of nearly singular integrals has seriously hindered the application of the boundary element method to the analysis of the physical quantities in the coating-structures. Herein, the analytical formulations for the nearly singular integrals in potential boundary integral equations developed by the authors before are generalized to the multi-domain system. This multi-domain boundary element method, in which the nearly singular integrals have been cracked, is introduced to analyze the temperature field in anisotropic coating-structures. The numerical examples demonstrate that the present method can model the temperature field in the coating-structure with much thinner coating in contrast with the conventional boundary element method. For the cases there are no analytical solutions available, the solutions from the finite element method are given out as the referenced ones. The temperature fields obtained by the present method can approach to the finite element solutions perfectly when the coating is very thin. The present method is versatile for the temperature analysis of the isotropic, orthotropic and anisotropic coating-structures.