Stress Concentrations in Thin Spherical Shells

Stress distributions occurring in the proximity of rigid circular inserts attached to thin spherical shells are reported in this paper. The solutions are achieved by employing conical coordinates tangent to the sphere at its intersection with the insert. A small-deflection theory is used and results are stated in terms of readily available functions. For convenience in practical applications, solutions for several loading conditions are carried through to completion. Specifically, the paper gives formulas for stress distributions occurring in a spherical shell when provided with a rigid insert and when subjected to (a) internal pressurization in the shell; (b) axial load on the insert; (c) external moment on the insert; and (d) tangential shear load on the insert. The necessary constants of integration are given in tables and the procedure developed is illustrated by a comprehensive example.