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

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

2009-01-26

arxiv.org/abs/0901.4041v1

Mathematics

Analysis of PDEs

21 pages

Scientific paper

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 $\det F\to0$.

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