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 of order h^4, converge to critical points of the Gamma-limit of h^{−4}E^h. This is proved under the physical assumption that the energy density blows up as the determinant of the deformation gradient tends to zero.
Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density
Mora, M. G.;
2012-01-01
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 of order h^4, converge to critical points of the Gamma-limit of h^{−4}E^h. This is proved under the physical assumption that the energy density blows up as the determinant of the deformation gradient tends to zero.File in questo prodotto:
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