Dynamic Stability Boundaries for Shallow Arches

The interactive effects of multiple dynamic loads on the snap-through instability of shallow elastic arches are investigated. Impulse loads and step loads of infinite duration are considered. The loads are applied either as concentrated loads at the quarter points of the arch, or as concentrated loads at the third points together with a uniformly distributed load. The arch is sinusoidal and has pinned ends. Critical load combinations, based on the Budiansky-Roth criterion, are computed numerically and plotted as interaction curves (i.e., stability boundaries). Curves of constant maximum response are also presented. The results for step loads are compared to the static critical loads, while the critical impulse loads are compared to some lower bounds. In addition, a single concentrated load at an arbitrary position of the arch is treated, and the locus of critical loads is determined for various arch rises. Both for step and impulse loads, the positions corresponding to minimum critical load are usually near the third points of the arch.