On the equilibrium of a cylindrical elastic solid: Comparisons with St. Venant's theory
type: Item
instance of: scholarly article
title: On the equilibrium of a cylindrical elastic solid: Comparisons with St. Venant's theory
zbMATH Open document ID: 0668.73006
DOI: 10.1007/BF00251499
author: G. Grioli
published in: Archive for Rational Mechanics and Analysis
publication date: 1989-01-01T00:00:00Z
review text: The author considers a linearly elastic cylinder of length 2h submitted to end tractions. In a first part, after establishing some identities on stress means, he derives a quadratic functional of the stress that has the property of being minimized by the stress of the Saint Venant solution. This functional is used to compute explicit lower bounds on the stored energy in terms of applied forces in the cases of extension, uniform flexion and torsion. In a second part, a general notion of ``overall strain'' is proposed, which is the least square rigid motion interpolate of the relative displacements of the ends of the cylinder. Explicit formulae for this overall strain in terms of applied forces are given. A comparison with Saint Venant's theory is effected. It shows that, in some instances, these formulae agree with the latter theory when \(h\to \infty\).
reviewed by: Hervé Le Dret
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 74G50
zbMATH DE Number: 4094916
zbMATH Keywords: linearly elastic cylinder
zbMATH Keywords: end tractions
zbMATH Keywords: quadratic functional of the stress
zbMATH Keywords: minimized by the stress of the Saint Venant solution
zbMATH Keywords: lower bounds on the stored energy
zbMATH Keywords: extension
zbMATH Keywords: uniform flexion
zbMATH Keywords: torsion
zbMATH Keywords: overall strain
zbMATH Keywords: least square rigid motion interpolate
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00251499
OpenAlex ID: W2024009252
description: scientific article; zbMATH DE number 4094916