Calculus of Variations and Geometric Measure Theory
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M. G. Mora - L. Scardia

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

created by mora on 25 Jan 2009
modified on 14 Oct 2011

[BibTeX]

Published Paper

Inserted: 25 jan 2009
Last Updated: 14 oct 2011

Journal: J. Differential Equations
Volume: 252
Pages: 35-55
Year: 2012

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 ${\mathcal E}^h$, whose energies (per unit thickness) are bounded by $Ch^4$, converge to critical points of the Gamma-limit of $h^{-4}{\mathcal E}^h$. This is proved under the physical assumption that the energy density $W(F)$ blows up as the determinant of F tends to zero.

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


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