Nonsymmetric Deformation of Dome-Shaped Shells of Revolution

Bending solutions that are uniformly valid in both shallow and nonshallow regions of a dome with arbitrary meridian are determined for edge loads that vary sinusoidally in the circumferential direction. The membrane and inextensional deformation solutions are obtained in terms of a function which satisfies a simple integral equation which eliminates the usual trial-and-error method of isolating the solutions that are regular at the apex. For a specific application, curves and formulas are obtained for the stresses and deformations of a dome with rigid rings clamped to the edges under the action of axial force, side force, and tilting moment.