Note on the Dynamic Buckling Loads of Shallow Spherical Shells from Static Analysis

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Abstract
If it is assumed that, during its forced vibrations which lead to dynamic axisymmetric snap-through buckling, a dynamically loaded spherical cap passes through one of its corresponding static, unstable equilibrium configurations, then it is possible to estimate the dynamic axisymmetric snap-through buckling load from a simple static analysis only, without resorting to an elaborate dynamic analysis. It is shown, through numerical analysis of the spherical cap subjected to a timewise step load, that dynamic axisymmetric snap-through buckling loads obtained from the static approach are comparable to those obtained from the dynamic approach.