Convergence of equilibria for incompressible elastic plates in the von Kármán regime

Marta Lewicka, Hui Li
2014 Communications on Pure and Applied Analysis  
We prove convergence of critical points to the nonlinear elastic energies J h of 3d thin incompressible plates, to critical points of the 2d energy obtained as the Γ-limit of J h in the von Kármán scaling regime. The presence of incompressibility constraint requires to restrict the class of admissible test functions to bounded divergence-free variations on the 3d deformations. This poses new technical obstacles, which we resolve by means of introducing 3d extensions and truncations of the 2d
more » ... iting deformations, specific to the problem at hand.
doi:10.3934/cpaa.2015.14.143 fatcat:wd6qgydw5zhfra5zxxevb23awi