Article
MSC:
35D99,
35Q72,
73F15,
73H05,
73K10,
74G60,
74K20 | MR 1052745 | Zbl 0727.73030 | DOI: 10.21136/AM.1990.104408
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Keywords:
von Kármán equations; viscoelastic plates; stability; plate of constant thickness; uniform compressive load; nonlinear functional analysis; operator; integro-operator formulations; post-buckling; circular plate
von Kármán equations; viscoelastic plates; stability; plate of constant thickness; uniform compressive load; nonlinear functional analysis; operator; integro-operator formulations; post-buckling; circular plate
Summary:
The paper deals with the analysis of generalized von Kármán equations which desribe stability of a thin circular viscoelastic clamped plate of constant thickness under a uniform compressible load which is applied along its edge and depends on a real parameter. The meaning of a solution of the mathematical problem is extended and various equivalent reformulations of the problem are considered. The structural pattern of the generalized von Kármán equations is analyzed from the point of view of nonlinear functional analysis.
References:
[1] J. Brilla: Stability Problems in Mathematical Theory of Viscoelasticity. in Equadiif IV, Proceedings, Prague, August 22-26, 1977 (ed. /. Fábera), Springer, Berlin-Heidelberg-New York 1979. MR 0535322
[2] Ľ. Marko: Buckled States of Circular Plates. Thesis, 1985 (Slovak).
[3] Ľ. Marko: The Number of Buckled States of Circular Plates. Aplikace matematiky, 34 (1989), 113-132. MR 0990299 | Zbl 0682.73036
[4] E. C. Titchmarsh: Eigenfunction Expansion Associated with Second-order Differential Equations. The Clarendon Press, Oxford 1958. MR 0094551
[5] F. G. Tricomi: Integral Equations. Interscience Publishers, New York 1957. MR 0094665 | Zbl 0078.09404
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