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
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
MSC-Numbers: 74K20, 74B20, 49J45
Keywords and phrases: nonlinear elasticity, plate theories, von Karman equations, equilibrium configurations, stationary points
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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 , whose energies (per unit thickness) are bounded by , converge to critical points of the -limit of . This is proved under the physical assumption that the energy density W blows up as .