A Basic Problem in Thermoelasticodynamics and its Solution

Abstract

Dynamic stresses in a solid sphere, brought about by a sudden temperature rise uniformly distributed over the whole volume of the sphere, is studied as a basic problem in thermoelasticodynamics. Using a simple reduction, the problem is first reduced to an isothermal dynamicresponse one. Exact solution to this dynamic response problem, for a hollow sphere with a fixed inner boundary, is developed with use of a solution in D’Alembertform and a technique of singularity extraction. This hollow sphere solution is further employed in a limit process, in which the inner radius of the sphere tends towards zero, with the objective of thereby creating a solution for the solid sphere. This limit process results in a solid sphere solution, which is exact and explicit, and takes various closed forms for each wave propagation and reflection. Numerical result and discussion regarding this solid sphere solution are given.