Study of the Symmetrical Elastic Loading of Some Shells of Revolution, with Special Reference to Toroidal Elements

Abstract

The governing equations for the elastic behaviour of axisymmetrically loaded thin elastic shells of revolution are derived and applied particularly to toroidal shells where the radius of revolution is much larger than the radius of ring cross-section. It is shown that under these conditions the approximate equations are a special case of the Mathieu type. Some solutions have recently been tabulated enabling the theory to be applied to structures such as toroidal pressure-vessel heads, expansion bellows and similar shapes. Comparison is made with an approximate series solution of the same equations.