Analytical solutions for thermoelastic stress-focusing in cylindrical and spherical solids

Abstract

This work deals with finding the analytical displacements and stresses in thermoelasticity problems involving solid isotropic cylinders and spheres with an emphasis on stress-focusing phenomena relevant to the nuclear industry and high-temperature engineering. The study considers solid spheres and infinitely long solid cylinders with three different types of thermal loading: prescribed outer surface temperature, prescribed surface heat flux, and volumetric heat source. Both continuous and discontinuous thermal loading conditions are considered. It is shown that discontinuous loading, such as abrupt changes in prescribed surface temperature or heat flux prescriptions, results in unbounded stresses along the axis (in the case of an infinite cylinder) and the center (in the case of a solid sphere), while with continuous loading, we obtain finite stresses within the domains at all times.