Anisotropic finite element estimates and local locking for shells: parabolic case

✍ Scribed by Jacqueline Sanchez-Hubert; Évariste Sanchez-Palencia

• Publisher: Elsevier Science
• Year: 2001
• Tongue: French
• Weight: 110 KB
• Volume: 329
• Category: Article
• ISSN: 1620-7742
• DOI: 10.1016/s1620-7742(01)01311-3

✦ Synopsis

We consider a thin shell with thickness 2ε with developable middle surface. A boundary is free along a generator. The loading is normal and non-zero along this generator. The energy concentrates inside a thin layer with thickness O(η), η = ε 1/4 . The structure of the layer is described by a penalty problem so that a locking phenomenon may appear. We give estimates of the error for the approximation with anisotropic finite elements of step O(H) and O(ηH) along and accross the layer respectively. For the same error, the corresponding triangulation includes a number of elements smaller, in the ratio η, to that of an isotropic mesh. The form and intensity of the terms of the local locking are made evident.  2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS thin shells / error estimates / boundary layer / anisotropic finite elements

Estimation de l'erreur pour des éléments finis anisotropes et verrouillage local dans les coques : cas parabolique

Résumé.