Analysis of Spherical Shells with Stress Functions

The homogenous equations of thin spherical shells are reduced, through the stress function and strain compatibility formulation, to two linear partial differential equations of fourth and sixth order, respectively, without any approximations other than those inherent in the initial equations and with the inclusion of transverse shear deformability. The elementary states of stress, known as the membrane, inextensional and edge zone states of stress, are each expressed in terms of one stress function and a corresponding differential equation. Two edge zone states of stress are obtained, one of which is completely associated with transverse shear deformability.