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Frictionless Contact of a Functionally Graded Half-Space and a rigid Base with an Axially Symmetric Recess

Published online by Cambridge University Press:  05 May 2011

S. P. Barik ,
M. Kanoria  and
P. K. Chaudhuri
S. P. Barik*
Affiliation:
Departmemt of Mathematics, Gobardanga Hindu College, Khantura, 24-Parganas (N), West Bengal, India
M. Kanoria*
Affiliation:
Department of Applied Mathematics, University of Calcutta 92, A.P.C. Road, Kolkata 700009, India
P. K. Chaudhuri*
Affiliation:
Department of Applied Mathematics, University of Calcutta 92, A.P.C. Road, Kolkata 700009, India
*
* corresponding author
** Professor
** Professor
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Abstract

This paper is concerned with an axially symmetric frictionless contact between an elastically transversely isptropic functionally graded half-space and a rigid base that has a small axisymmetric surface recess. The graded half-space is modeled as a nonhomogeneous medium. We reduce the problem to solving Fredholm integral equations, solve these equations numerically and establish a relationship between the applied pressure and gap radius. The effects of anisotropy and nonhomogeneity parameter of the graded half-space on the normal pressure as well as on the critical pressure have been shown graphically.

Keywords

Functionally graded materialTransversely isotropic mediumHankel transformFredholmintegral equation.
Type
Articles
Information
Journal of Mechanics , Volume 25 , Issue 1 , March 2009 , pp. 9 - 18
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2009

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References

1.Sneddon, I. N. and Lowengrub, M., Crack Problems in the Classical Theory of Elasticity, John Wiley, New York (1969).Google Scholar
2.Gladwell, G. M. L., Contact Problems in the Classical Theory of Elasticity, Sijthoff and Noordhoff, alphen aan den Rijin (1980).Google Scholar
3.Selvanduri, A. P. S., “The Body Force Inducing Separation at a Frictionless Precompressed Transversely Isotropic Interface,” Trans. Can. Mech. Eng., 7, pp. 154–157 (1983).CrossRefGoogle Scholar
4.Wu, E. and Yen, C. S., “The Contact Behavior Between Laminated Composite Plates and Rigid Spheres,” J. Appl. Mech., 61, p. 60 (1994).CrossRefGoogle Scholar
5.Shvets, R. M., Martynyak, R. M. and Kryshtofovych, A. A., “Discontinuous Contact of an Anisotropic Half-Plane and a Rigid Base with Disturbed Surface,” Int. J. Engg. Sci., 34, pp. 183–200 (1996).CrossRefGoogle Scholar
6.Brock, L. M. and Georiadis, H. G., “An Illustration of Sliding Contact at Any Constant Speed on Highly Elastic Half-Spaces,” IMA J. Appl. Math., 66, pp. 551–566 (2001).CrossRefGoogle Scholar
7.Kit, G. S. and Monastyrsky, B. E., “A Contact Problem for a Half-Space and a Rigid Base with an Axially Symmetric Recess,” J. Mathematical Sciences, 107, pp. 3545–3549 (2001).CrossRefGoogle Scholar
8.Argatov, I. I., “Asymptotic Modelling of the Contact Interaction Between a System of Rigidly Connected Punches and an Elastic Base,” Sib. Zh. Ind. Math., 3, pp. 10–22 (2000).Google Scholar
9.Argatov, I. I., “The Method of Averaging in a Contact Problem for a System of Punches,” J. Appl. Math. and Mech., 68, pp. 93–104 (2004).CrossRefGoogle Scholar
10.Barik, S. P., Kanoria, M. and Chaudhuri, P. K., “Contact Problem for an Anisotropic Elastic Layer Lying on an Anisotropic Elastic Foundation Under Gravity,” J. Indian Acad. Math., 28, pp. 205–223 (2006).Google Scholar
11.Ke, L.-L., and Wang, Y.-S., “Two Dimensional Sliding Frictional Contact of a Functionally Graded Materials,” European J. Mechanics A/Solids, 26, pp. 171–188 (2007).CrossRefGoogle Scholar
12.Birinci, A. and Erdol, R., “Frictionless Contact Between a Rigid Stamp and an Elastic Layered Composite Resting on Simple Supports,” Mathematica and Computational Applications, 4, pp. 261–272 (1999).CrossRefGoogle Scholar
13.Chaudhuri, P. K. and Ray, S., “Receding Axisymmetric Contact Between a Transversely Isotropic Layer and a Transversely Isotropic Half-Space,” Bull. Cal. Math. Soc., 95, pp. 151–164 (2003).Google Scholar
14.Chaudhuri, P. K. and Ray, S., “Receding Contact Between an Orthotropic Layer and an Orthotropic Half-Space,” Archives of Mechanics, 50, pp. 743–755 (1998).Google Scholar
15.Comez, I., Birinci, A. and Erdol, R., “Double Receding Contact Problem for a Rigid Stamp and Two Elastic Layers,” European J. of Mechanics A/Solids, 23, pp. 909–924 (2004).CrossRefGoogle Scholar
16.El-borgi, S., Abdelmoula, R. and Keer, L., “A Receding Contact Plane Problem Between a Functionally Graded Layer and a Homogeneous Substrate,” Int. J. Solids and Structures, 43, pp. 658–674 (2006).CrossRefGoogle Scholar
17.Jing, H. S. and Liao, M. L., “An Improved Finite Element Scheme for Elastic Contact Problems with Friction,” Computers and Structures, 35, pp. 571–578 (1990).CrossRefGoogle Scholar
18.Garrido, J. A., Foces, A. and Paris, F., “B.E.M. Applied to Receding Contact Problems with Friction,” Mathematical and Computer Modeling, 15, pp. 143–154 (1991).CrossRefGoogle Scholar
19.Paris, F., Blazquez, A. and Canas, J., “Contact Problems with Nonconforming Discretizations Using Boundary Element Method,” Computers and Structures, 57, pp. 829–839 (1995).CrossRefGoogle Scholar
20.Satish Kumar, K., Dattaguru, B., Ramamurthy, T. S. and Raju, K. N., “Elasto-Plastic Contact Stress Analysis of Joints Subjected to Cyclic Loading,” Computers and Structures, 60, pp. 1067–1077 (1996).Google Scholar
21.Garrido, J. A. and Lorenzana, A., “Receding Contact Problem Involving Large Displacements Using the BEM,” Engineering Analysis with Boundary Elements, 21, pp. 295–303 (1998).CrossRefGoogle Scholar
22.Ozturk, M. and Erdogan, F., “The Axisymmetric Crack Problen in a Non-Homogeneous Medium,” J. Appl. Mech., 60, pp. 406–413 (1993).CrossRefGoogle Scholar
23.Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Body, Mir Publishers, Moscow (1981).Google Scholar
24.Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series, and Products, Academic Press (1963).Google Scholar
25.Erdogan, F. and Gupta, G. D., “On the Numerical Solution of Singular Integral Equations,” Q. Appl. Math., 29, pp. 525–534 (1972).CrossRefGoogle Scholar
26.Lusher, C. P. and Hardy, W. N., “Axisymmetric Free Vibrations of a Transversely Isotropic Finite Cylindrical Rod,” J. Appl. Mech., 55, pp. 855–862 (1985).CrossRefGoogle Scholar