# Decomposition of the deformations of a thin shell. Nonlinear elastic models

Abstract : We investigate the behavior of the deformations of a thin shell, whose thickness $\delta$ tends to zero, through a decomposition technique of these deformations. The terms of the decomposition of a deformation $v$ are estimated in terms of the $L^2$-norm of the distance from $\nabla v$ to $SO(3)$. This permits in particular to derive accurate nonlinear Korn's inequalities for shells (or plates). Then we use this decomposition technique and estimates to justify a nonlinear bending model for elastic shells for an elastic energy of order $\delta^3$.
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https://hal.archives-ouvertes.fr/hal-00373296
Contributor : Dominique Blanchard <>
Submitted on : Friday, April 3, 2009 - 5:19:03 PM
Last modification on : Wednesday, December 9, 2020 - 3:10:24 PM
Long-term archiving on: : Friday, October 12, 2012 - 4:11:14 PM

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Blanchard-Griso_Janv09_.pdf
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• HAL Id : hal-00373296, version 1

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Dominique Blanchard, Georges Griso. Decomposition of the deformations of a thin shell. Nonlinear elastic models. 2008. ⟨hal-00373296⟩

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