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Effects of an axisymmetric rigid punch on a nonhomogeneous transversely isotropic half-space

Published online by Cambridge University Press:  17 February 2009

P. K. Chaudhuri  and
Subhankar Ray
P. K. Chaudhuri
Affiliation:
Department of Applied Mathematics, University College of Science, 92 A.P.C.Road, Calcutta 700 009, India; e-mail: pkcha@vsnl.net.
Subhankar Ray
Affiliation:
Department of Applied Mathematics, University College of Science, 92 A.P.C.Road, Calcutta 700 009, India; e-mail: pkcha@vsnl.net.
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Abstract

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Elastic behaviour of a nonhomogeneous transversely isotropic half-space is studied under the action of a smooth rigid axisymmetric indentor. Hankel transforms of different orders have been used. It is observed that in contrast to a homogeneous medium, the pressure distribution in the contact region in a nonhomogeneous medium is not directly available, rather it is obtainable from the solution of a Fredholm integral equation. The integral equation is solved for a flat-ended punch and paraboloidal indentations for various values of the nonhomogeneity parameter, and the effects of nonhomogeneity in elastic behaviour on stresses have been shown graphically. The results of the associated homogeneous case are readily available from the results of the present study.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 3 , January 2003 , pp. 461 - 474
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Danyluk, H. T., Singh, B. M. and Vrbik, J., “The Reissner-Sagoci problem for a non-homogeneous half-space with a penny-shaped crack”, J. Engrg. Math. 29 (1995) 437–449.CrossRefGoogle Scholar
[2]Dhaliwal, R. S. and Singh, B. M., “The axisymmetric Boussinesq problem of an initially stressed Neo-Hookean half-space for a punch of arbitrary profile”, Int. J. Engrg. Sci. 16 (1978) 379–385.CrossRefGoogle Scholar
[3]Gladwell, G. M. L., Contact problems in the classical theory of elasticity (Sijthoff and Noordhoff, 1980).CrossRefGoogle Scholar
[4]Gradshteyn, I. S. and Ryzhik, I. M., Table of integrals, series and products (Academic Press, New York, 1980) 682, 731.Google Scholar
[5]Hassan, H. A. Z. and Rofaeel, F. E. K., “Reissner-Sagoci problem for a non-homogeneous half-space with surface constraint”, J. Engrg. Math. 28 (1994) 117–127.CrossRefGoogle Scholar
[6]Lekhnitskii, S. G., Theory of elasticity of an anisotropic body (Mir, Moscow, 1981).Google Scholar
[7]Ozturk, M. and Erdogan, F., “An axisymmetric crack in bonded materials with a nonhomogeneous interfacial zone under torsion”, J. Appl. Mech. 62 (1995) 116–125.CrossRefGoogle Scholar
[8]Pouyet, J. and Lataillade, J. L., “Elastic strain of a transversely isotropic half-space caused by a rigid punch”, Lett. Appl. Engrg. Sci. 17 (1979) 765–772.Google Scholar
[9]Sneddon, I. N., “The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile”, Int. J. Engrg. Sci. 3 (1965) 47–57.CrossRefGoogle Scholar
[10]Spence, D. A., “Self-similar solutions to adhesive contact problems with incremental loading”, Proc. Roy. Soc. A 305 (1968) 55–80.Google Scholar
[11]Spence, D. A., “A Wiener-Hopf equation arising in elastic contact problems”, Proc. Roy. Soc. A 305 (1968) 81–92.Google Scholar
[12]Ting, T. C. T., “The contact stresses between a rigid indenter and a viscoelastic half-space”, J. Appl. Mech. 33 (1966) 845–854.CrossRefGoogle Scholar