Dynamic Instability of a Deep Spherical Shell

Axisymmetrical snapping of a thin elastic deep spherical shell under a suddenly applied constant dynamic loading distributed uniformly over the surface of the shell is considered on the basis of finite-deformation theory. Based on a first approximation of deflections, qualitative results are obtained by using a phase-plane method. It is found that the critical dynamic pressure of such a shell can be considerably lower than the static critical pressure predicted by classic linear theory. In addition, there is the possibility of the occurrence of a jump at an applied pressure even lower than the critical value because of finite disturbance. It is suggested that the dynamic buckling pressure be found statistically based on experimental results.