Publications
2009
Issue 15

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

15/2009

Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density

Maria Giovanna Mora and Lucia Scardia

Abstract

The asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $E^{h}$ , whose energies (per unit thickness) are bounded by $C h^{4}$ , converge to critical points of the $Γ$ -limit of $h^{- 4} E^{h}$ . This is proved under the physical assumption that the energy density $W$ blows up as $det F \to 0$ .

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Received:: 16.03.09

Published:: 24.03.09

MSC Codes:: 74K20, 74B20, 49J45

Keywords:: nonlinear elasticity, plate theories, von Karman equations, equilibrium configurations, stationary points

Related publications

inJournal

2012 Repository Open Access

Maria Giovanna Mora and Lucia Scardia

Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density

In: Journal of differential equations, 252 (2012) 1, pp. 35-55

BibTex DOI: 10.1016/j.jde.2011.09.009 ArXiv: 0901.4041