The exact moment for the plastic torsion of a cylindrical bar of elliptical cross section
type: Item
instance of: scholarly article
title: The exact moment for the plastic torsion of a cylindrical bar of elliptical cross section
zbMATH Open document ID: 0588.73058
DOI: 10.1007/BF01176374
published in: Acta Mechanica
publication date: 1986-01-01T00:00:00Z
review text: An exact expression for the limiting moment of the torsion of an isotropic, perfectly plastic elliptical bar has not been previously derived. In this note, the solution of this classical problem is reduced in form to a single quadrature. It is shown by comparison that an approximation due to \textit{V. V. Sokolovsky} [Theory of plasticity (German) (1955; Zbl 0067.174)] is inaccurate for large aspect ratios of semiaxes. Through a transformation of coordinates, the exact solution is also applicable to the plastic torsion of an orthotropic circular cylinder with generators perpendicular to a principal axis. It follows that for highly orthotropic materials an approximate solution derived by \textit{R. Hill} [J. Mech. Phys. Solids 2, 87-91 (1954)] may also prove inaccurate.
Mathematics Subject Classification ID: 74R20
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 3945463
zbMATH Keywords: limiting moment
zbMATH Keywords: torsion
zbMATH Keywords: isotropic, perfectly plastic elliptical bar
zbMATH Keywords: single quadrature
author: David J. Unger
MaRDI profile type: Publication
cites work: Q5801127
cites work: Q3235109
cites work: Q5808115
cites work: Q3228191
cites work: Q5673486
cites work: Q4275389
full work available at URL: https://doi.org/10.1007/bf01176374
OpenAlex ID: W2160557632
description: scientific article; zbMATH DE number 3945463