Thermoelastic dynamic solution of a multilayered spherically isotropic hollow sphere for spherically symmetric problems

Abstract

The thermoelastic dynamic solution of a multilayered spherically isotropic hollow sphere in the state of spherical symmetry is obtained. By the method of superposition, the displacement is divided into two parts: one is quasi-static and the other is dynamic. The quasi-static solution is first derived in an explicit form by using the transfer matrix method. Then by introducing a new dependent variable, the governing equations, boundary conditions as well as the initial conditions for the dynamic solution are rewritten, and the dynamic solution is obtained by the separation of variables method coupled with the initial parameter method as well as the orthogonal expansion technique. The present method is suitable for a multilayered spherically isotropic hollow sphere consisting of arbitrary layers and subjected to arbitrary spherically symmetric thermal loads. Numerical results are finally presented and discussed.