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

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 ${\mathcal{E}}^h$, whose energies (per unit thickness) are bounded by $C{h}^4$, 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 $\det F\to 0$.

21 pages