关键词: 广义热弹性, 功能梯度材料(FGM), Green-Lindsay理论, 矢量-矩阵微分方程, Bellman方法

Abstract: This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). The surface of cavity is stress-free and is subjected to a time-dependent thermal shock. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Bellman method. Displacement, stress and temperature are computed and presented graphically. It is found that variation in the thermo-physical properties of a material strongly influences the response to loading. A comparative study with a corresponding homogeneous material is also made.

Key words: generalized thermoelasticity, functionally graded material (FGM), Green-Lindsay theory, vector-matrix differential equation, Bellman method