Koiter Estimate Revisited

Monique Dauge, Erwan Faou.

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 S of the shell is an arbitrary smooth manifold with boundary.

The bound of our energy estimate only involves the thickness parameter ε, constants attached to S, the loading, the two-dimensional energy of the solution of the Koiter model and ``wave-lengths'' associated with this latter 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.

Rennes, 5 janvier 2008
Prépublication IRMAR 08-01

Math. Models Methods Appl. Sci. 20, 1, pp. 1-42 DOI: 10.1142/S0218202510004131

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