Non-linear static and dynamic instability of complete spherical shells using mixed finite element formulation

Abstract

The finite element method based on the total Lagrangian description of the motion and the Hellinger–Reissner principle with independent strain is applied to investigate the non-linear static and dynamic responses of spherical laminated shells under external pressure. The non-linear dynamic problem is solved by employing the implicit time integration method. The critical load of thin spherical laminated panels is investigated by examining the static and dynamic responses. The critical dynamic load is determined by the phase-plane and the Budiansky–Roth criteria. The effect of the artificial coefficient of Rayleigh damping on the dynamic response is considered. The dynamic response with damping included converges to the static response. The damping coefficient greatly affects a highly non-linear dynamic response. For a thin spherical panel with the snapping phenomena, the critical dynamic load is lower than the static one.