Preprint 15/2009

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

Maria Giovanna Mora and Lucia Scardia

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Submission date: 16. Mar. 2009
Pages: 23
published in: Journal of differential equations, 252 (2012) 1, p. 35-55 
DOI number (of the published article): 10.1016/j.jde.2011.09.009
Bibtex
MSC-Numbers: 74K20, 74B20, 49J45
Keywords and phrases: nonlinear elasticity, plate theories, von Karman equations, equilibrium configurations, stationary points
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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 formula12, whose energies (per unit thickness) are bounded by formula14, converge to critical points of the formula16-limit of formula18. This is proved under the physical assumption that the energy density W blows up as formula22.

23.06.2018, 02:12