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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