Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-08T09:49:36.461Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Chree, C.Trans. Cambridge Philos. Soc. 14 (1889), 250.Google Scholar
(2)Conway, H. D. and Farnham, K. A.Internat. J. Engrg. Sci. 5 (1967), 541.CrossRefGoogle Scholar
(3)Filon, L. N. G.Philos. Trans. Roy. Soc. Lond. Ser. A 198 (1902), 147.Google Scholar
(4)Green, A. E., Rivlin, R. S. and Shield, R. T.Proc. Roy. Soc. London Ser. A 211 (1952), 128.Google Scholar
(5)Green, A. E. and Zerna, W.Theoretical elasticity, 2nd ed. (Oxford, 1968).Google Scholar
(6)Sneddon, I. N.Fourier transforms (McGraw-Hill N.Y., 1951).Google Scholar
(7)Sneddon, I. N.Mixed boundary value problems in potential theory (North-Holland Publishing Company, Amsterdam, 1966).Google Scholar
(8)Sokolnikoff, I. S.Mathematical theory of elasticity (2nd ed.) (New York; McGraw-Hill, 1956).Google Scholar
(9)Spillers, W. R.J. Math. and Phys., 43 (1964), 65.CrossRefGoogle Scholar
(10)Titchmarsh, E. C.Theory of fourier integrals (2nd ed.) (Oxford: Clarendon Press, 1948).Google Scholar
(11)Tranter, C. J. and Craggs, J. W.Philos. Mag. 36 (1945), 241.CrossRefGoogle Scholar
(12)Vaughan, H.Proc. Roy. Soc. London Ser. A 321 (1971), 381.Google Scholar