Critical displacements are determined for snap-through of shallow, extensible, and elastic arches that are pushed downward quasi-statically 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 push-down 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.
Snap-Through of Shallow Extensible Arches Under Unilateral Displacement Control
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 3, 2015; final manuscript received May 30, 2015; published online June 18, 2015. Assoc. Editor: Kyung-Suk Kim.
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Plaut, R. H. (September 1, 2015). "Snap-Through of Shallow Extensible Arches Under Unilateral Displacement Control." ASME. J. Appl. Mech. September 2015; 82(9): 094503. https://doi.org/10.1115/1.4030741
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