On Nonsymmetric Dynamic Problems of Elastic Spherical Shells

Abstract

Homogeneous separable solutions are derived for the deformation of thin spherical shells explicitly in terms of Legendre functions. These solutions are exact within the scope of the theory of shells in which the effects of transverse shear and rotatory inertia are fully accounted for. It is shown how the solutions are calculated from their hypergeometric series. For application, the problem of an open spherical shell with a rigid insert subjected to horizontal force and/or moment is solved in detail, and the numerical results are compared with those given earlier for shallow shells and for spherical shells with a large insert.