Contact Problem for an Elastic Layered Composite Resting on Rigid Flat Supports

Authors: T. S. Ozsahin, V. Kahya, A. Birinci, A. O. Cakiroglu

Abstract:

In this study, the contact problem of a layered composite which consists of two materials with different elastic constants and heights resting on two rigid flat supports with sharp edges is considered. The effect of gravity is neglected. While friction between the layers is taken into account, it is assumed that there is no friction between the supports and the layered composite so that only compressive tractions can be transmitted across the interface. The layered composite is subjected to a uniform clamping pressure over a finite portion of its top surface. The problem is reduced to a singular integral equation in which the contact pressure is the unknown function. The singular integral equation is evaluated numerically and the results for various dimensionless quantities are presented in graphical forms.

Keywords: Frictionless contact, Layered composite, Singularintegral equation, The theory of elasticity.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1329943

References:

[1] Civelek, M.B., Erdogan, F., ''The frictionless contact problem for an elastic layer under gravity'', Journal of Applied Mechanics, vol. 42, pp. 136, 1975.
[2] Civelek, M.B., Erdogan, F., ''Interface separation in a frictionless contact problem for an elastic layer'', Journal of Applied Mechanics, vol. 43, pp. 175, 1976.
[3] Civelek, M.B., Erdogan, F., Cakiroglu, A.O., ''Interface separation for an elastic layer loaded by a rigid stamp'', International Journal of Engineering Science, vol. 16, pp. 669, 1978.
[4] Cakiroglu, A.O., ''Contact problem for plates on elastic half plane'', Thesis (in Turkish), Civil Engineering Department, KTU, 1979.
[5] Cakiroglu, A.O., Cakiroglu, F.L., ''Continuous and discontinuous contact problems for strips on an elastic semi-finite plane'', International Journal of Engineering Science, vol. 29, pp. 99, 1991.
[6] Civelek, M.B., Erdogan, F., ''The axisymmetric double contact problem for frictionless elastic layer'', International Journal of Solid and Structures, vol. 10, p.p. 639, 1974.
[7] Gecit, M.R., Gokpinar, S., ''Frictionless contact between an elastic layer and a rigid rounded support'', The Arabian Journal for Science and Engineering, vol. 10, p.p. 243, 1984.
[8] Gecit, M.R., Yapici, H., ''Contact problem for an elastic layer on rigid flat supports'', The Arabian Journal for Science and Engineering, vol. 11, p.p. 235, 1984.
[9] Sneddon, I.N., The Use of Integral Transforms, McGraw-Hill, New York, 1972.
[10] Muskhelishvili, N.I., Singular Integral Equations, Noordhoff, Groningen, 1958.
[11] Erdogan, F., Gupta, G.D., ''On the numerical solution of singular integral equations'', Quarterly Journal of Applied Mathematics, vol. 29, p.p. 525, 1972.