Transient Thermoelastic Problem for a Transversely Anisotropic Hollow Sphere with Temperature-Dependent Properties

Abstract

This paper is concerned with a polar symmetric transient thermoelastic problem for a transversely anisotropic hollow sphere, the boundary of internal surface being subjected to sudden temperature rise. The problem is treated on assumption that the thermal and elastic properties of the sphere are dependent on temperature. Basic equation is solved with the aid of perturbation method. The particular boundary value problems are solved, and the corresponding displacements and stresses are clarified. For numerical examples, calculations are performed on the cases of anisotropic spheres made of grades ATJ and ZTA graphites respectively. In these treatments, the variation of conductivity and thermal expansion is assumed to be linear according to the temperature rise, but that of the Young's moduli is assumed to be quadratic. The solution for an isotropic sphere is also derived as a particular case of the present problem.