Convergence of Equilibria for Incompressible Elastic Plates in the von Kármán Regime

Abstract

We prove convergence of critical points $u^h$ of the nonlinear elastic energies $E^h$ of thin incompressible plates ${\Omega }^h=\Omega \times (-h/2,h/2)$, which satisfy the von Kármán scaling: $E^h(u^h)\le C{h}^4$, to critical points of the appropriate limiting (incompressible von Kármán) functional.