Abstract
A constructive method is developed to establish the existence of buckled states of a thin, flat elastic plate that is rectangular in shape, simply supported along its edges, and subjected to a constant compressive thrust applied normal to its two short edges. Under the assumption that the stress function and the deformation of the plate are described by the nonlinear von Kármán equations, the approach used yields information regarding not only the number of buckled states near an eigenvalue of the linearized problem, but also the continuous dependence of such states on the load parameter and the possible selection of that buckled state “preferred” by the plate. In particular, the methods used provide a rigorous approach to studying the existence of buckled states near the first eigenvalue of the linearized problem (that is, near the “buckling load”) even when the first eigenvalue is not simple.
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Communicated by J. B. McLeod
This research was supported in part by the United States Army under contract No. DA-31-124-ARO-D-462 and was completed while the second author was a Senior Visiting Fellow at the University of Strathclyde during the North British Differential Equations Year sponsored by the Science Research Council of the United Kingdom.
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Knightly, G.H., Sather, D. Nonlinear buckled states of rectangular plates. Arch. Rational Mech. Anal. 54, 356–372 (1974). https://doi.org/10.1007/BF00249196
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DOI: https://doi.org/10.1007/BF00249196