Plastic Buckling of Point-Loaded Spherical Shells

The effects of inelastic strains on the deflection and stability of thin spherical domes with roller-supported edges under point loads at the apex are studied analytically and experimentally. The governing nonlinear differential equations are derived by applying Reissner's nonlinear shell theory and the total deformation theory of plasticity. These equations are solved by a finite difference scheme using Newton's method. Four domes, hydroformed from 6061-0 aluminum, are tested. It is concluded that the inelastic strains do account for most of the discrepancies existing between the analytically predicted (based on elastic analysis alone) and the experimentally observed shell responses. It is found that for certain geometric configurations (i.e., λ > 6) the local existence of finite strains and significant strain reversal indicates that closer correlation between theory and experiment is possible using an incremental plasticity theory.