A Galerkin approximation for linear elastic shallow shells

✍ Scribed by I. N. Figueiredo; L. Trabucho

• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 775 KB
• Volume: 10
• Category: Article
• ISSN: 0178-7675
• DOI: 10.1007/bf00369855

✦ Synopsis

Thls work is a generalization to shallow shetl models of previous results for plates by B. Miara (1989). Using the same basis functions as in the plate case, we construct a Galerkin approximation of the three-dimensional linearized elasticity problem, and establish some error estimates as a function of the thickness, the curvature, the geometry of the shell, the forces and the Lam~ constants.

1 Geometry of the shell and some notations

In the following, greek indices y fl, #,.. will belong to the set { 1, 2}, latin indices i,j, k .... will belong to the set { 1, 2, 3} and the usual summation convention on the repeated index will be adopted. We assume that an orthonormal basis {ei} is given in the Euclidean space R 3. We will denote by 0 (xl, x2, x3) a generic point in ~x 3 and define the operator 0i = --. 0xi Ler co~ be a surface in IR 3, that is the image of an open, bounded, connected subset co~R 2, with a Lipschitz continuous boundary, by a mapping 0 ~ = 0~ei:~ ~, IR 3 smooth enough, that depends on the positive real parameter e, and such that