Some Remarks on Spherical Shells

Abstract

The present paper treats the deformation of a spherical shell within the framework of a linear bending theory which includes the effect of transverse-shear deformation. A two-term asymptotic solution of the governing equations is obtained which embraces all terms of an order retained in the formulation of the theory. The solution is valid within a physically important domain of the shell and reduces to the previously known one-term asymptotic solution of the classical bending theory. The problem of variable thickness is also discussed. The behavior of the thickness function may be such as to require in the solution a correction term which may contribute significantly to the deformation. This solution is applied to a treatment of the deformation of a rotating, completely closed spherical shell stiffened by an annular disk located normal to the axis of the spin.