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An axisymmetric contact problem: the constriction of elastic cylinders under axial compression

Published online by Cambridge University Press:  24 October 2008

Henry Vaughan  and
Derek Allwood
Henry Vaughan
Affiliation:
Institute of Applied Mathematics, The University of British Columbia
Derek Allwood
Affiliation:
Institute of Applied Mathematics, The University of British Columbia
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Abstract

The compression of fairly short solid cylinders under axial load is considered. Radial expansion is prevented over a central region of the outer surface by a rigid constraint concentric with the cylinder. Physically the situation arises when a fairly soft rivet is expanded into a relatively rigid plate. Two types of elastic material are considered; firstly, rubber-like materials governed by a strain energy function of the Mooney form, and secondly, metals which have a quadratic strain energy function. In the former case a finite axial compression is permitted prior to contact between the cylinder and the constraint. In both cases the irregularities introduced by the constraint are sufficiently small that they can be described by infinitesimal elasticity theory. The analysis utilizes displacement potential functions and is reduced to solving a set of dual cosine series. The particular case in which the cylinder height and diameter are equal and the contact height is equal to the radius is examined in detail and the contact stresses are given graphically.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 3 , November 1972 , pp. 499 - 514
Copyright
Copyright © Cambridge Philosophical Society 1972

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