Cylindrical Shells Under Partially Distributed Radial Loading

The elastic solution to the fundamental problem of a cylindrical shell subjected to a symmetric, partially distributed, and self-balanced radial pressure loading acting on the external surface is obtained under plane strain condition. A dual series approach based on Airy’s stress functions is employed yielding an exact solution to an auxiliary composite cylindrical assembly problem. The solution for the problem under study is then derived as a limit case of the auxiliary composite cylinder problem. It is proven that the more generalized solution presented here may be used to recover several well-known classical results. The solutions also agree very well with the numerical results obtained from a finite element analysis performed for one sample hollow shell problem. The rigorous expressions found in this analysis for the stress and displacement fields are applicable to both thin and thick-walled shells, including piping.