Convergence of equilibria of thin elastic plates - the von Kármán case

Stefan Müller and Mohammed Reza Pakzad

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Submission date: 12. Mar. 2007
Pages: 13
published in: Communications in partial differential equations, 33 (2008) 6, p. 1018-1032 
DOI number (of the published article): 10.1080/03605300701629443
Bibtex
MSC-Numbers: 74K20, 74B20
Keywords and phrases: Equilibria, plates, nonlinear elasticity, von Karman equations
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Abstract:
We study the behaviour of thin elastic bodies of fixed cross-section and of height h, with . We show that critical points of the energy functional of nonlinear three-dimensional elasticity converge to critical points of the von Kármán functional, provided that their energy per unit height is bounded by (and that the stored energy density function satisfies a technical growth condition). This extends recent convergence results for absolute minimizers.