A problem on slender nearly cylindrical shells suggested by Torroja's structures

Abstract

In this paper we consider peculiar kinds of curved slender nearly cylindrical elastic shells enjoying rigidity properties inherited from the geometry which furnish remarkable properties of strength. In two previous papers were addressed the cases exactly cylindrical and slightly hyperbolic (i.e. the total curvature of the middle surface is zero or slightly negative). In the present work, we take advantage of a new kind of a priori estimates which is independent of the type (either hyperbolic or elliptic) of the middle surface, allowing a generalization of the results to more general surfaces, including the elliptic case (i.e. with curvature slightly positive).