Secondary buckling analysis of spherical caps

The aim of this paper is to investigate the secondary buckling behaviour and mode-coupling of spherical caps under uniformly external pressure. The analysis makes use of a rotational finite shell element on the basis of strain-displacement relations according to Koiter\'s shell theory (Small Finite Deflections). The post-buckling behaviours after a bifurcation point are analyzed precisely by considering multi-mode coupling between several higher order harmonic wave numbers: and on the way of post-buckling path the positive definiteness of incremental stiffness matrix of uncoupled modes is examined step by step. The secondary buckling point that has zero eigen-value of incremental stiffness matrix and the corresponding secondary mode are obtained, moreover, the secondary post-buckling path is traced.