Buckling Analyses of Spherical Shells by the Finite Element Method Based on the Willis-Form Equations

Abstract

Buckling analysis of spherical shells under external pressure is a crucial problem in mechanical and aerospace engineering. It is widely known that the buckling loads obtained by classical methods are much higher than experimental results. The main reason for this large discrepancy is customarily attributed to initial geometrical imperfections, and the impact of inhomogeneously distributed stresses during loading process is usually ignored. In order to investigate the effect of this ignored factor, the buckling loads of several spherical shells are analyzed by the geometrically nonlinear finite element method (FEM) based on the Willis-form equations, which explicitly contain the stress gradients at previous loading step. It can be shown that the buckling loads from the Willis-form FEM are about 10% lower than the values from classical FEM. This finding may give better understandings to the differences between theoretical and experimental results for nearly perfect spherical shells and may be helpful to obtain more accurate buckling loads for shells with initial geometrical imperfections.