Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-27T15:54:18.544Z Has data issue: false hasContentIssue false
  • English
  • Français

Contact problem of an elastic plug in an elastic region

Published online by Cambridge University Press:  17 February 2009

G. P. Steven
G. P. Steven
Affiliation:
Department of Aeronautical Engineering, The University of Sydney, Sydney, N.S.W., 2006, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The contact problem investigated in this paper may be more fully described as a three dimensional elastic body with a circular hole through it; inside this tunnel is press fitted a solid elastic plug of finite length. Shear stresses are taken to be absent along the contact interface.

An influence coefficient technique is used to model the governing integral equation. For the elastic region the displacement influence coefficients due to bands of constant pressure are determined using a numerical quadrature on Fourier integrals. However, the plug, being of finite length, requires the superposition of two separate solutions to boundary value problems before the displacement influence coefficients can be determined.

Contact pressure distributions are presented for a sample of parameter variations and also for a case where hydrostatic pressure is present in the tunnel in the elastic region. Despite both components being elastic the imposition of a constant interference displacement along the interface still gives rise to the characteristic singularity in contact pressure at the edges of contact due to the strain discontinuity at these points.

Type
Research Article
Information
The ANZIAM Journal , Volume 19 , Issue 2 , December 1975 , pp. 229 - 241
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Benthem, J. P. and Minderhoud, P., Int. J. Solids. Struct. 8 (1972) 1027.CrossRefGoogle Scholar
[2]Blair, J. M. and Veeder, J. I., J. of Appl. Mech. 36 (1969) 241.CrossRefGoogle Scholar
[3]Chandrashekhara, K., AIAA J. 7 (1969) 1161.CrossRefGoogle Scholar
[4]Conway, H. D. and Farnham, K. A., Int. J. of Engng. Sci. 5 (1967) 541.CrossRefGoogle Scholar
[5]Conway, H. D. and Farnham, K. A., Int. J. of Mech. Sci. 10 (1968) 757.CrossRefGoogle Scholar
[6]Eubanks, R. A., Proc. 8th Midwest. Mech. Conf. 2 (1963) 84.Google Scholar
[7]Galerkin, M. B., Compres Rendus. Acad. Sci., Paris 190 (1930) 1047.Google Scholar
[8]Galin, L. A., Contact Problems in the Theory of Elasticity, North Carolina State College (1961).Google Scholar
[9]Hodgkins, W. R., UKAEA TRG Rpt. 294 (1962).Google Scholar
[10]Horvay, G. and Mirabal, J. A., J. Appl. Mech. 25 (1958) 561.CrossRefGoogle Scholar
[11]Kaehler, H., AIAA J. 3 (1965) 2132.CrossRefGoogle Scholar
[12]Klemm, J. L. and Little, R. W., SIAM J. Appl. Maths. 19 (1970) 712.CrossRefGoogle Scholar
[13]Little, R. W. and Childs, S. B., O. Appl. Math. 25 (1967) 261.Google Scholar
[14]Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, Dover, (1944).Google Scholar
[15]Lur'e, A. I., Three Dimensional Problems in the Theory of Elasticity, Interscience (1964).Google Scholar
[16]Mendelson, A. and Roberts, E., Midwest. Tech. Conf. Case. Inst. Tech. (1963).Google Scholar
[17]Neuber, H., Angew, Z.. Math. Mech. 14 (1934).Google Scholar
[18]Okubo, H., Z. Angew. Math. Mech. 12 (1952) 178.CrossRefGoogle Scholar
[19]Papkovich, P. F., Izvest. Akad. Nauk. SSSR, 10 (1932)Google Scholar
also Comptes Rendus. Acad. Sci. Paris, 192 (1932) 513.Google Scholar
[20]Powers, L. D. and Childs, S. B., Int. J. Engng. Sci. 9 (1970) 241.CrossRefGoogle Scholar
[21]Sadowsky, M. A., Trans. ASME, paper no. APM–54–21 (1932) 221.Google Scholar
[22]Severn, R. T., Q. J. Mech. Appl. Math. 12 (1952) 178.Google Scholar
[23]Shibahara, M. and Oda, J., Bull. JSME 11 (1968) 1000.CrossRefGoogle Scholar
[24]Steven, G. P., D. Phil Thesis, The University of Oxford (1970).Google Scholar
[25]Steven, G. P., Int. J. of Engng. Sci. 11 (1973) 795.CrossRefGoogle Scholar
[26]Swan, G. W., SIAM J. Appl. Math. 16 (1968) 860.CrossRefGoogle Scholar
[27]Tranter, C. J., Quart. J. of Appl. Maths. 4 (1964) 298.CrossRefGoogle Scholar
[28]Warren, W. E. and Roark, A. L., AIAA J. 5 (1967) 1484.CrossRefGoogle Scholar
[29]Warren, W. E., Roark, A. L. and Bickford, W. B., AIAA J. 5 (1967) 1448.CrossRefGoogle Scholar
[30]Westergaard, H. M., Karman Anniversary Volume, (1941) 154.Google Scholar
[31]Widera, O. E. and Wu, C. H., J. Engng. Maths. 2 (1968) 343.CrossRefGoogle Scholar