A Contact Problem of an Elastic Layer Compressed by Two Punches of Different Radii

Document Type: Research Paper

Authors

Department of Mechanical Engineering, Faculty of Technology, University of Batna2, Algeria

Abstract

The elasticity mixed boundary values problems dealing with half-space contact are generally well resolved. A large number of these solutions are obtained by using the integral transformation method and methods based the integral equations. However, the problems of finite layer thicknesses are less investigated, despite their practical interests. This study resolves a quasi-stationary problem of an isotropic elastic layer compressed by two rigid cylinders with flat ends. Hankel transformation and auxiliary functions with boundary conditions reduce the differential equation to an algebraic equations system, which can be solved in a numerical way. The contact efforts equations are established. From the general method, solutions of particular cases are also resolved. A particular case is studied, the contact zone pressure and stresses distribution curves are presented.

Keywords

[1] Harding J.W., Sneddon I.N., 1945, The elastic stresses produced by the indentation of the plane surface of a semi-infinite elastic solid by a rigid punch, proceedings of the Cambridge Philosophical Society 41: 16-26.
[2] Ufliand Ja.S., 1965, Survey of Articles on the Applications of Integral Transforms in the Theory of Elasticity, Defense Technical Information Center, North Carolina State University.
[3] Kuz’min Iu.N., Ufliand Ia.S., 1967, The contact problem of an elastic layer compressed by two punches, Journal of Applied Mathematics and Mechanics 31(4): 711-715.
[4] Zakorko V.N., 1978, Contact problem for a layer with two stamps, Journal of Applied Mathematics and Mechanics 42(6): 1068-1073.
[5] Dhaliwal R.S., Sing B.M., 1977, Axisymmetric contact problem for an elastic layer on a rigid foundation with a cylindrical hole, International Journal of Engineering Science 15: 421-428.
[6] Ufljand Ia.S., 1963, Integral Transforms in Elasticity Problems, Nauka. SSR.
[7] Sneddon I.N., 1959, A note on the axially symmetric punch problem, Mathematika 6: 118-119.
[8] Sneddon I.N., 1977, Application of Integral Transforms in the Theory of Elasticity, CISM Courses and lectures, Springer-Verlag Vien, New York.
[9] Kuo C.H., Keer L., 1992, Contact stress analysis of a layered transversely isotropic half-space, ASME Journal of Tribology 114: 253-262.
[10] Matnyac S.V., 2003, Contact stresses distribution under a rigid cylinder rolling over a pre-stressed strip, International Applied Mechanics 39(7): 840-847.
[11] Shelestovshii B.G., Gabrusev G.V., 2004, Thermoelastic state of a transversely isotropic layer between two annular punches, International Applied Mechanics 40(4): 67-77.
[12] Ruiny C., Dahan M., 2002, Chargements axisymétriques d’un bicouche transversalement isotrope, Mécanique 330 : 469-473.
[13] Grilitskii D.V., Kizima Y., 1981, Theory of Deformation Elastic and Thermic, Axisymetric Contact Problem, Nauka, Moscow.
[14] Argatov I.I., Dmitriev N.N., 2003, Fundamentals of the Theory of Elastic Discrete Contact, St. Polytechnics, St. Petersburg, Russian.
[15] Gradshteyn I.I., Ryzhik I.M., 1980, Tables of Integrals, Series, and Products, Academie press, New York.
[16] Seghir K., Benbouta R., Balbacha El., 2010, Analysis of stresses in the contact zone Rigid cylindrical indenter – transversely isotropic elastic layer, Matériaux & Techniques 98: 227-232.
[17] Ditkin V.A., Prudnikov V.A., 1965, Integral Transforms and Operational Calculus, Pergamon Press, New York.