Koiter Estimate Revisited

Monique Dauge (1) , Erwan Faou (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IPSO - Invariant Preserving SOlvers

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.

Domaines: Analyse numérique [math.NA]

Monique Dauge, Erwan Faou. Koiter Estimate Revisited. 2008. ⟨hal-00202628v1⟩