Two-Mode Buckling of an Elastically Supported Plate and Its Relation to Catastrophe Theory

[+] Author and Article Information
D. Hui, J. S. Hansen

Institute of Aerospace Studies, University of Toronto, Downsview, Ontario, Canada M3H 5T6

J. Appl. Mech 47(3), 607-612 (Sep 01, 1980) (6 pages) doi:10.1115/1.3153741 History: Received February 01, 1979; Revised October 01, 1979; Online July 21, 2009


Classical buckling and initial postbuckling of a geometrically imperfect infinite plate on a nonlinear elastic foundation under two independent applied compressive loads are analyzed. The plate is assumed to have imperfections of the same form as the buckling modes. It is found that single mode behavior occurs when the two independent loads Nx and Ny are unequal. A two-mode case occurs when the two applied loads are equal and the form of the instability falls into the category of the parabolic umbilic type one or type two, depending on the quadratic and cubic spring constants. The importance of the contribution of the quartic term and imperfection-sensitivity is examined. The analysis is studied within the context of Koiter’s general theory of multimode postbuckling behavior.

Copyright © 1980 by ASME
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