Local estimation of the error in the von Mises' stress and L2‐norm of the stress for linear elasticity problems

L. Gallimard (Laboratoire de Mécanique de Paris X, France)

Engineering Computations

ISSN: 0264-4401

Publication date: 1 December 2006

Abstract

Purpose

This paper aims to focus on the local quality of outputs of interest computed by a finite element analysis in linear elasticity.

Design/methodology/approach

In particular outputs of interest are studied which do not depend linearly on the solution of the problem considered such as the L2‐norm of the stress and the von Mises' stress. The method is based on the concept of error in the constitutive relation.

Findings

The method is illustrated through 2D test examples and shows that the proposed error estimator leads in practice to upper bounds of the output of interest being studied.

Practical implications

This tool is directly usable in the design stage. It can be used to develop efficient adaptive techniques.

Originality/value

The interest of this paper is to provide an estimation of the local quality of L2‐norm of the stress and the Von Mises' stress as well as practical upper bounds for these quantities.

Keywords

Citation

Gallimard, L. (2006), "Local estimation of the error in the von Mises' stress and L2‐norm of the stress for linear elasticity problems", Engineering Computations, Vol. 23 No. 8, pp. 876-897. https://doi.org/10.1108/02644400610707775

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Publisher

:

Emerald Group Publishing Limited

Copyright © 2006, Emerald Group Publishing Limited

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