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arXiv · 1502.03924

Plate theory as the variational limit of the complementary energy functionals of inhomogeneous anisotropic linearly elastic bodies

Francois Murat·Roberto Paroni
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Abstract

We consider a sequence of linear hyper-elastic, inhomogeneous and fully anisotropic bodies in a reference configuration occupying a cylindrical region of height epsilon. We then study, by means of Gamma-convergence, the asymptotic behavior as epsilon goes to zero of the sequence of complementary energies. The limit functional is then identified as a dual problem for a two-dimensional plate. Our approach gives a direct characterization of the convergence of the equilibrating stress fields.

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Francois Murat, Roberto Paroni. 2015-02-13. Plate theory as the variational limit of the complementary energy functionals of inhomogeneous anisotropic linearly elastic bodies. https://arxiv.org/abs/1502.03924

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