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Stability and secondary bifurcation for von Kármán plates

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Summary

The Movchan-Liapunov theorem is used to establish a sufficiency criterion for stability of equilibrium configurations of the von Kármán plate under edge loads and displacements. This criterion is used to characterize the possible occurrence of secondary bifurcation from the first buckled state of the perfect plate. A Koiter-Fitch post-bifurcation analysis of the secondary solution leads to a tentative explanation of the mode-jumping phenomenon that is observed experimentally. A numerical study of the rectangular plate for various aspect ratios is given. For this example, the base solution is represented as a perturbation power series in an appropriate load parameter.

Zusammenfassung

Der Movchan-Liapunov Lehrsatz wird benutzt, um ein Zulänglichkeitskriterion für die Stabilität von Gleichgewichtskonfigurationen der von Kármán Platte bei Randbelastungen und Verschiebungen herzustellen. Dieses Kriterion wird benutzt, um den möglichen Eintritt sekundärer Gabelung vom ersten verbogenen Zustand der perfekten Platte zu charakterisieren. Eine Koiter-Fitch Nachgabelungsanalyse der Sekundärlösung führt zu einer tentativen Erklärung des sprunghaften Konfigurationswechsels, den man experimentell beobachtet. Eine numerische Untersuchung der rechteckigen Platte für verschiedene Längenverhältnisse ist gegeben. Für diese Beispiele wird die Primärlösung als Störungspotenzreihe im angemessenen Belastungsparameter gegeben.

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Authors and Affiliations

  1. IBM Corporation, 55901, Rochester, Minnesota

    G. J. Stroebel

  2. Department of Aerospace Engineering and Mechanics, University of Minnesota, 55455, Minneapolis, Minnesota

    W. H. Warner

Authors
  1. G. J. Stroebel
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  2. W. H. Warner
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Additional information

This paper is based in part upon the thesis submitted by the first author to the University of Minnesota in partial fulfillment of the requirements for the Ph. D. degree. Support given by a NASA traineeship is gratefully acknowledged.

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Stroebel, G.J., Warner, W.H. Stability and secondary bifurcation for von Kármán plates. J Elasticity 3, 185–202 (1973). https://doi.org/10.1007/BF00052893

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  • DOI: https://doi.org/10.1007/BF00052893

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