Snap-through of arches and buckled beams under unilateral displacement control

Arches and beams buckled upward are analyzed. The structure is pushed downward from above at a specific location along the span until snap-through occurs and the structure jumps to an inverted equilibrium shape. Each beam or arch is modeled as an inextensible elastica. Critical displacements are computed for buckled beams with both ends pinned, both ends clamped, or one end clamped and the other end pinned. Circular arches with pinned ends are also investigated. The ends are immovable. The critical displacement is obtained directly from a theoretical equilibrium shape of the initial unloaded structure. Numerical results are presented for four height-to-span ratios of the initial structure, showing the critical displacement for any application point along the span. At the onset of snap-through, the imposed displacement is at or below the horizontal chord connecting the ends.