This paper presents a new integral equation for 2D and 3D thermal stress analysis of structures consisting of functionally graded materials. Using this equation together with the three-step multi-domain BEM technique, thermal stress analysis can be carried out for complicated structures comprised of arbitrarily many numbers of media with varying material properties. The Kelvin fundamental solutions independent of elastic modulus are used in this paper. As a result, the resulting integral equations include domain integrals due to the non-homogeneity and temperature variations of the material. All these domain integrals are transformed into equivalent boundary integrals using the radial integration method (RIM), resulting in a pure boundary element analysis algorithm. Finally, two numerical examples are given on 2D and 3D thermal stress analysis of two typical thermal protection systems for space shuttles to verify the correctness of the proposed formulation by comparing computational results with those obtained by the finite element method.%导出了一种新的可对功能梯度材料结构进行二维和三维热应力分析的积分方程,利用该方程并结合多区域边界元三步求解技术,可对由任意多种介质组成的变物性参数复合结构进行热应力分析;采用与弹性模量无关的Kelvin解作为问题的基本解,导出的积分方程含有由材料的非均质性以及温度变化引起的域积分;使用径向积分法将所有的域积分转换成等价的边界积分,从而建立起只需要边界离散的无内部网格边界元算法;最后对两种典型的飞行器防热结构进行二维和三维热应力算例分析,并通过与有限元计算结构对比验证结果的正确性.
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