Decomposition of the deformations of a thin shell. Asymptotic behavior of the Green-St Venant's strain tensor
Résumé
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 give the asymptotic behavior of the Green-St Venant's strain tensor when the {\it ''strain energy''} is of order less than $\delta^{3/2}$.
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