Elastodynamic solution for spherically symmetric problems of a multilayered hollow sphere

The elastodynamic solution of a multilayered hollow sphere for spherically symmetric problems is obtained by decomposition into two parts, one being the quasi-static and the other the dynamic solution. The quasi-static solution is firstly derived by means of the state-space method, and the dynamic solution is obtained by utilizing the separation of variables method and the orthotropic expansion technique. The solutions for displacement and stresses are obtained in result. The present method is suitable for a multilayered spherically isotropic hollow sphere, with arbitrary thickness of each of the layers and arbitrary initial conditions, subjected to arbitrary form of a spherically symmetric dynamic load at the internal and external surfaces. Numerical results are finally presented.