Thin Circular Conical Shells Under Arbitrary Loads

Abstract

Abstract Equations defining the displacements of the median surface of a conical shell under arbitrary loads are developed. In their derivation only the essential parts of the strain energy are considered and three simultaneous partial differential equations are obtained through the use of the variational calculus. When the minimum radius of curvature of the median surface of the cone is made to approach a constant value, the cone goes over into a cylinder. At the same time the equations here developed for the cone are transformed into the Donnell equations of the theory of cylindrical shells. It is shown how eigenfunctions of the homogeneous equations can be constructed and how particular solutions can be found for any arbitrary loading.