Dynamic Buckling of Shallow Arches

A summary is given of a theoretical study of the symmetric and asymmetric dynamic buckling behavior of a shallow arch subjected to symmetric, uniformly distributed dynamic loads. The approach used approximates the arch equations by finite differences and solves the resulting nonlinear differential equations by numerical integration. Symmetric dynamic buckling loads are calculated for an ideal impulse, a step load of finite or infinite duration, and an infinite duration load pulse with finite rise times. The effect of load duration and rise time on the critical load is determined. A new criterion is proposed to determine the asymmetric dynamic buckling load of symmetrically loaded structures. By use of this criterion, the buckling load of an arch subjected to a uniformly distributed initial impulse is calculated. Asymmetric dynamic buckling loads may be substantially less than the corresponding critical symmetric loads, and there appear to be parameter ranges for an undamped arch where the critical load for asymmetric dynamic buckling approaches zero.