Analysis of thermoelastic response in a functionally graded spherically isotropic hollow sphere based on Green–Lindsay theory

Abstract

This paper is concerned with the investigation of thermoelastic displacements and stresses in a functionally graded spherically isotropic hollow sphere due to prescribed temperature in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). Both the surfaces of the body are free from radial stresses, and the inner surface is subjected to a time-dependent thermal shock whereas the outer one is maintained at constant temperature. 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. The numerical inversion of the transforms is carried out using a method of Bellman et al. The displacements and stresses are computed and presented graphically. It is found that the variation of the thermophysical properties of a material as well as the thickness of the body strongly influence the response to loading. A comparative study with the corresponding homogeneous material has also been made. The solution of the problem of a spherically isotropic infinite medium containing a spherical cavity has been derived theoretically by tending the outer radius to infinity, as a particular case.