Closed-form solutions for the elastic–plastic buckling design of shell structures under external pressure

Abstract

This paper deals with the elastoplastic buckling analysis of shell geometries traditionally encountered in pressure vessels subjected to external pressure loading. The objective is to propose in a unified way original analytical closed-form solutions giving rise to reliable results, with a good accuracy and a wide range of applications in a straightforward and low time-consuming way, for efficient dimensioning purposes. The present study is based on the plastic bifurcation theory, classically used in the context of conservative systems, where additional terms are incorporated here due to the follower external pressure acting normally to the deformed surface of the shell still after buckling. Cylindrical shells are first considered, which certainly represent the most fundamental components of pressure vessels in practice. Owing to the external pressure also acting on the closure ends of a cylinder, the influence of the induced axial compression is investigated thereafter. It appears to be non-negligible for short cylinders in elasticity and it becomes very significant in the case of plastic buckling. Then, closed-form solutions for the critical external pressure of a complete sphere are also obtained, both in elasticity and plasticity. Finally, all these new closed-form solutions are validated against reference numerical results obtained through finite element computations, and compared to current design rules.