A justification of linear Koiter and Naghdi's models for totally clamped shell

Article type: Research Article

Authors: Lods, Véronique | Mardare, Cristinel^;

Affiliations: Laboratoire d'Applications des Mathématiques, Téléport 2, 86960 Futuroscope, France E‐mail: [email protected]‐poitiers.fr | Laboratoire d'Analyse Numérique, Université Paris VI, 4, place Jussieu, 75005 Paris, France E‐mail: [email protected]

Note: [] Corresponding author.

Abstract: We consider a shell, i.e., a three‐dimensional body with a small thickness (denoted by 2ε), which is clamped along its entire lateral boundary and subjected to regular loads. In the linear case, one can use the two‐dimensional models of Koiter or Naghdi to calculate the displacement vector field of the shell. Some error estimates have been obtained in [12,13] between these models and the three‐dimensional displacement for flexural or membrane shells. Here, we do not make any assumptions on the geometry of the shell. In particular, the space of inextensional displacements can be reduced to zero. The assumptions on the loads are weak: for the sake of simplicity, one can consider regular loads (in H1) which do not depend on the transverse variable. We then establish a relative error estimate for the scaled linearized deformation tensor between Koiter's model (or Naghdi's model) and the three‐dimensional model. These estimates hold though the limit model is not always known. In addition, further assumptions on the data allow to recover the error estimates concerning the displacements which have been proved in [12,13].

Journal: Asymptotic Analysis, vol. 31, no. 3-4, pp. 189-210, 2002