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Reports (Research Report) Year : 2003

Multiscale Expansions for Linear Clamped Elliptic Shells

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.

Domains

Other [cs.OH]
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Dates and versions

inria-00071623 , version 1 (23-05-2006)

Identifiers

  • HAL Id : inria-00071623 , version 1

Cite

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