Benchmark analytic solution of the dynamic response of a spherical shell composed of a transverse isotropic elastic material

Developing benchmark analytic solutions for problems in solid and fluid mechanics is very important for the purpose of testing and verifying computational physics codes. In order to test the numerical results of physics codes, we consider the geometrically linear dynamic sphere problem. We present an exact solution for the dynamic response of a spherical shell composed of a linearly elastic material exhibiting transverse isotropic symmetry. The solution takes the form of an infinite series of eigenfunctions. We demonstrate, both qualitatively and quantitatively, the convergence of the computed benchmark solution under spatial, temporal, and eigenmode refinement.