Stability of Complete Circular and Non-Circular Toroidal Shells

Abstract

In the first part of the paper a comparison of various theoretical methods for predicting the elastic buckling pressures of externally pressurized complete circular toroidal (that is doughnut shaped) shells is given. Calculations were also carried out using the BOSOR 5 shell buckling program. The accuracy of the latter was checked using two independent programs. The available experimental results on toroidal shells, from the United States and Russia, are summarized and their buckling pressures calculated using BOSOR 5. A simple equation for predicting the buckling pressures of these shells, due to Jordan, is also briefly reviewed. The buckling of externally pressurized complete elliptical toroidal shells is then discussed. Both buckling pressures and buckling modes for selected geometries are given. Depending on the major/minor axis ratio, the buckling pressures of the elliptical toroids can be larger or smaller than those of the corresponding circular toroids. Some part-cylindrical, part-spherical cross-sections were also explored. Buckling due to internal pressure is considered in the third part of the paper. It is predicted to occur for several complete toroids of elliptical cross-section. It is believed that this is a new result. It still has to be verified experimentally.