A Galerkin approximation for curved beams
type: Item
instance of: scholarly article
title: A Galerkin approximation for curved beams
zbMATH Open document ID: 0767.73094
DOI: 10.1016/0045-7825(93)90110-J
author: Luís Trabucho
author: Isabel N. Figueiredo
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1993-06-29T00:00:00Z
review text: We apply a Galerkin method to the equations of linearized three- dimensional elasticity for a curved beam. We explicitly construct an approximate solution of the three-dimensional elasticity problem as a minimizer of the \(H^ 1\) norm with respect to a geometric parameter. This is done by replacing the three-dimensional elasticity problem by a series of two- and one-dimensional problems, which are easier to solve. We prove that the approximation error in the \(H^ 1\) norm is a function of the loading, the geometry, the order of approximation and the curvature and torsion tensors associated with the definition of the beam axis.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 219613
zbMATH Keywords: linearized three-dimensional elasticity
zbMATH Keywords: minimizer
zbMATH Keywords: approximation error
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 219613