Thermal stresses in an orthotropic hollow sphere under thermal shock: a unified generalized thermoelasticity

This paper deals with the thermoelasticity problem in an orthotropic hollow sphere. A unified governing equation is derived which includes the classical, Lord-Shulman and Green-Lindsay coupled theories of thermoelasticity. Time-dependent thermal and mechanical boundary conditions are applied to the inner and outer surfaces of the hollow sphere and the problem is solved analytically using the finite Hankel transform. The inner surface of the sphere is subjected to a thermal shock in the form of a prescribed heat flux. Subsequently, the thermal response, radial displacement, as well as radial, tangential, and circumferential stresses of the sphere are determined. The influence of different orthotropic material properties and relaxation time values is investigated and presented graphically. The obtained results demonstrate excellent agreement with the existing literature.