Convergence of equilibria for incompressible elastic plates in the von Kármán regime
Marta Lewicka, Hui Li · Communications on Pure & Applied Analysis · 2015
We prove convergence of critical points to thenonlinear elastic energies $J^h$ of 3d thin incompressibleplates, to critical points of the 2d energy obtained as the$\Gamma$-limit of $J^h$ in the von Kármán scaling regime.The presence of incompressibility constraint requires to restrict the class ofadmissible test functions to bounded divergence-freevariations on the 3d deformations.This poses new technical obstacles, which we resolve by means ofintroducing 3d extensions and truncations of the 2d limitingdeformations, specific to the problem at hand.