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
|Pdf file HAL|