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MiS Preprint
27/2007

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

Stefan Müller and Mohammed Reza Pakzad

Abstract

We study the behaviour of thin elastic bodies of fixed cross-section and of height $h$, with $h \to 0$. We show that critical points of the energy functional of nonlinear three-dimensional elasticity converge to critical points of the von K\'arm\'an functional, provided that their energy per unit height is bounded by $C h^4$ (and that the stored energy density function satisfies a technical growth condition). This extends recent convergence results for absolute minimizers.

Received:
Mar 12, 2007
Published:
Mar 12, 2007
MSC Codes:
74K20, 74B20
Keywords:
Equilibria, plates, nonlinear elasticity, von Karman equations

Related publications

inJournal
2008 Repository Open Access
Stefan Müller and Mohammad Reza Pakzad

Convergence of equilibria of thin elastic plates : the von Karman case

In: Communications in partial differential equations, 33 (2008) 6, pp. 1018-1032