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Koiter Estimate Revisited

Monique Dauge 1 Erwan Faou 2
2 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : We prove a universal energy estimate between the solution of the three-dimensional Lamé system on a thin clamped shell and a displacement reconstructed from the solution of the classical Koiter model. The mid-surface of the shell is an arbitrary smooth manifold with boundary. The bound of our energy estimate only involves the thickness parameter, constants attached to the midsurface, the loading, the two-dimensional energy of the solution of the Koiter model and ''wave-lengths'' associated with this solution. This result is in the same spirit as Koiter's who gave a heuristic estimate in 1970. Taking boundary layers into account, we obtain rigorous estimates, which prove to be sharp in the cases of plates and elliptic shells.
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Submitted on : Friday, May 19, 2006 - 8:55:45 PM
Last modification on : Friday, May 20, 2022 - 9:04:52 AM
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  • HAL Id : inria-00070577, version 1


Monique Dauge, Erwan Faou. Koiter Estimate Revisited. [Research Report] RR-5430, INRIA. 2004, pp.35. ⟨inria-00070577⟩



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