Snap Through of Shallow Extensible Arches Under Unilateral Displacement Control

Abstract

Critical displacements are determined for snapthrough of shallow, extensible, and elastic arches that are pushed downward quasistatically at any point along the span. The initial arch is circular and unstrained, and the ends of the arch are pinned and immovable. When the vertical position at the pushdown location reaches a critical value, the arch jumps into an inverted shape (unless the arch is extremely shallow). The critical displacement is given or approximated by an unstable equilibrium configuration of the unloaded arch, for which an analyical formula is derived.