Two- and three-dimensional results for rotationally symmetric deformations of circular cylindrical shells

Abstract

Previous considerations by asymptotic expansion procedures of the relation between elasticity theory results and thin-shell theory results for the case of rotationally symmetric deformations of an edge-loaded semi-infinite circular cylindrical shell are supplemented by an analysis of this problem for a shell possessing a limiting-type orthotropy, such that transverse normal strains vanish identically. It is shown that assuming this kind of orthotropy has the important benefit of allowing the derivation of exact expressions for the edge zone solution contribution, when such exact expressions are not possible for the problem of the shell with more general properties of the material. One result of the present analysis is an answer to the following question. Given a shell with arbitrarily prescribed edge displacements (compatible with the assumed type of orthotropy), what is the asymptotically exact form of the corresponding conditions for this same problem, treated within the framework of two-dimensional thin-shell theory?