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

Marta Lewicka; Hui Li

doi:10.3934/cpaa.2015.14.143

Article Contents

2015, Volume 14, Issue 1: 143-166. Doi: 10.3934/cpaa.2015.14.143

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

Marta Lewicka^1, and
Hui Li^2,

1.
University of Pittsburgh, Department of Mathematics, 301 Thackeray Hall, Pittsburgh, PA 15260
2.
2030 Mary Ellen Lane, State College, PA 16803

Received: February 28, 2014

Revised: March 31, 2014

Published: December 2014

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Abstract

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 $\Gamma$-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 limiting deformations, specific to the problem at hand.

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Mathematics Subject Classification: Primary: 74K20; Secondary: 74B20.

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