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


Published Paper

Inserted: 25 jan 2009
Last Updated: 14 oct 2011

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


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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