涂层结构中温度场的边界元解

涂层结构由于其优良的物理化学性能而备受人们关注，但受其厚度尺寸的影响，涂层材料中物理量的数值计算一直是工程中的难点。边界元法分析涂层结构时，难点在于涂层子域的数值分析，边界量计算既涉及奇异积分又涉及几乎奇异积分。本文基于间接规则化边界积分方程，准确高效地计算奇异边界积分。针对计算边界量及内点物理量时涉及的几乎奇异积分，采用一类非线性变量替换法，有效地改善了被积函数的震荡特性，从而消除了积分核的几乎奇异性。通过采用二次单元逼近几何边界，使得高效准确地计算超薄的涂层结构成为可能。

BOUNDARY ELEMENT ANALYSIS OF THE TEMPERATURE FIELD IN COATING STRUCTURES

Materials containing thin coatings are frequently used for the design of many industrial applications, profiting from its excellent physical and chemical qualities. However, due to the small size of its thickness, numerical analysis of the behavior of these structures represents a great challenge to researchers in engineering applications. The key to analyze coating structure problems by using boundary element method (BEM) is the accurate computation of nearly singular integrals. In this paper, the coating structure is divided into the substrate domain and the coating one by using a multi-domain boundary element approach, and then a general transformation method has been introduced to remove or damp out the near singularities of the kernel integrals in the coating domain. Both temperatures and fluxes are accurately computed by using the present method. Numerical examples demonstrate that the present method can effectively deal with coating structure problems even when its thickness is as small as 1E-10.