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Convergence of equilibria of thin elastic plates - the von Kármán case
Stefan Müller and Mohammed Reza Pakzad
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.