Symmetric Buckling of Inelastic Spherical Shells

A numerical method for determining the buckling loads and stresses for elastic-plastic spherical shells subjected to uniform external pressure is presented. No restriction is placed on shallowness in the analysis. The incremental theory of plasticity and the von Mises yield criterion are used in formulating the problem. The governing differential equations are formulated in terms of displacements and are solved with the aid of finite differences, an incremental-iterative technique, and a high speed digital computer. Buckling loads are taken as the first maximum of a load-average deflection curve. Numerical results are presented for a clamped spherical shell. Buckling loads are compared to the elastic complete sphere value and the limit analysis load. The relationship of the radius-thickness ratio to buckling stress is presented.