Analytical solution of the thermoelasticity problem in a pressurized thick-walled sphere subjected to transient thermal loading

The thermoelasticity problem in a thick-walled sphere is solved analytically using finite Hankel transform. Time-dependent boundary conditions are prescribed on the inner surface of the sphere, where for the mechanical boundary conditions the tractions are prescribed on both the inner and the outer surfaces of the hollow sphere. Obtaining the distribution of the temperature throughout the sphere, the quasi-static and the dynamical structural problem is solved and closed-form relations are derived for stress components. On solving the dynamical thermoelasticity problem, a thermal shock was observed after plotting the results. Using the obtained plots, the velocity of the spherical dilatation wave is computed and compared with the one from the classical formula and the results are compared with those in the literature, where possible.