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Multiscale Expansions for Linear Clamped Elliptic Shells

Erwan Faou 1
1 ALADIN - Algorithms Adapted to Intensive Numerical Computing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : We investigate solutions of the two-dimensional Koiter model and of the three-dimensional linear shell model in the case where the shell is clamped and its mean surface is elliptic. For smooth data, these solutions admit multiscale expansions in powers of ε^1/2 where ε denotes the (half-)thickness of the shell. Both expansions contain terms independent of ε and boundary layer terms exponentially decreasing with respect to r/√ε, with r the distance to the boundary of the mean surface. The expansion of the three-dimensional displacement contains supplementary boundary layers, exponentially decreasing with respect to r/ε like for plates. Using these expansions we obtain sharp estimates between the two models in various norms.
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https://hal.inria.fr/inria-00071623
Contributor : Rapport de Recherche Inria <>
Submitted on : Tuesday, May 23, 2006 - 6:20:20 PM
Last modification on : Thursday, February 11, 2021 - 2:48:03 PM
Long-term archiving on: : Tuesday, February 22, 2011 - 11:59:31 AM

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  • HAL Id : inria-00071623, version 1

Citation

Erwan Faou. Multiscale Expansions for Linear Clamped Elliptic Shells. [Research Report] RR-4956, INRIA. 2003. ⟨inria-00071623⟩

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