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 general adimensional 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 two-dimensional Koiter model. This estimate only involves the thickness parameter ε, constants attached to the mid-surface, the two-dimensional energy of the solution of the Koiter model and ``wave-lengths'' associated with this latter solution. This bound is in the same spirit as Koiter's heuristic estimate (1970) and can be viewed as an a posteriori estimation of the modeling error by means of the two-dimensional solution. It is general with respect to the geometry of the mid-surface which is an arbitrary smooth manifold with boundary. Taking boundary layer terms into account, we prove that our estimates are sharp in the cases of plates and elliptic shells.

Mots clés: Shell; Koiter; asymptotics

Domaines: Analyse numérique [math.NA]

Monique Dauge, Erwan Faou. Koiter Estimate Revisited. Mathematical Models and Methods in Applied Sciences, 2010, 20 (1), pp. 1-42. ⟨10.1142/S0218202510004131⟩. ⟨hal-00202628v2⟩