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Technical Brief

Snap-Through of Shallow Extensible Arches Under Unilateral Displacement Control

[+] Author and Article Information
Raymond H. Plaut

Fellow ASME
Department of Civil and Environmental Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: rplaut@vt.edu

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.

J. Appl. Mech 82(9), 094503 (Sep 01, 2015) (2 pages) Paper No: JAM-15-1184; doi: 10.1115/1.4030741 History: Received April 03, 2015; Revised May 30, 2015; Online June 18, 2015

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.

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References

Plaut, R. H., 1979, “Influence of Load Position on the Stability of Shallow Arches,” J. Appl. Math. Phys. (ZAMP), 30(3), pp. 548–552. [CrossRef]
Cazottes, P., Fernandes, A., Pouget, J., and Hafez, M., 2009, “Bistable Buckled Beam: Modeling of Actuating Force and Experimental Validations,” ASME J. Mech. Des., 131(10), p. 101001. [CrossRef]
Chen, J.-S., and Hung, S.-Y., 2011, “Snapping of an Elastica Under Various Loading Mechanisms,” Eur. J. Mech. A, 30(4), pp. 525–531. [CrossRef]
Pandey, A., Moulton, D. E., Vella, D., and Holmes, D. P., 2014, “Dynamics of Snapping Beams and Jumping Poppers,” EPL, 105(2), p. 24001. [CrossRef]
Fargette, A., Neukirch, S., and Antkowiak, A., 2014, “Elastocapillary Snapping: Capillarity Induces Snap-Through Instabilities in Small Elastic Beams,” Phys. Rev. Lett. (PRL), 112(13), p. 137802. [CrossRef]
Harvey, P. S., Jr., and Virgin, L. N., 2015, “Coexisting Equilibria and Stability Boundaries of a Shallow Arch: Unilateral Displacement-Control Experiments and Theory,” Int. J. Solids Struct., 54(1), pp. 1–11. [CrossRef]
Plaut, R. H., 2015, “Snap-Through of Arches and Buckled Beams Under Unilateral Displacement Control,” Int. J. Solids Struct., 63(1), pp. 109–113. [CrossRef]
Bazant, Z. P., and Cedolin, L., 1991, Stability of Structures, Oxford University Press, New York.

Figures

Grahic Jump Location
Fig. 1

Three equilibrium shapes of unloaded arch for b = 5

Grahic Jump Location
Fig. 2

Critical displacement dcr as function of push-down location c for b = 3, 4, 5, and 6

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