Deformation of Elastic Paraboloidal Shells of Revolution

Abstract

Abstract The present paper, using the contributions to the theory of shells of revolution given recently by Naghdi (1), is concerned with the axisymmetric problem of thin elastic paraboloidal shells of revolution which includes the effect of transverse-shear deformation. Following the general scheme given in (1), an asymptotic solution is obtained for paraboloidal shells of uniform thickness and is valid at the apex of the shell. In the limit, these results reduce to the predictions of the classical theory of H. Reissner-Meissner. Solutions are given by both theories for a specific example, namely, a second-degree paraboloidal shell loaded uniformly over a small region about the apex when the open edge is clamped.