Abstract
We consider a system consisting of n elastic layers made of different transversely isotropic materials bonded to each other and the last layer bonded to an elastic half-space made of a different transversely isotropic material. An arbitrary tangential displacement is prescribed over a domain S of the first layer, while the rest of the layer’s surface is stress free. The tangential contact problem consists of finding the complete stress and displacement fields in this system. The Generalized Images method developed by the author is used to get an elementary solution to the problem. We first consider the case of two layers and then generalize it for the case of n layers. The same problem is solved by the integral transform method, and it is shown that an integral transform can be interpreted as a sum of generalized images. The results are valid for the case of isotropy as well.
Similar content being viewed by others
References
Lebedev NN, Ufliand IaS (1958) Axisymmetric contact problem of an elastic layer. J Appl Math Mech 22: 442–450
I.I.Vorovich II, Ustinov IaA (1959) Pressure of a die on an elastic layer of finite thickness. J Appl Math Mech 23: 637–650
Westmann RA (1965) Asymmetric mixed boundary-value problem of the elastic half-space. ASME J Appl Mech 32: 411–417
Fabrikant VI (1989) Applications of potential theory in mechanics. Selection of new results. Kluwer, Dordrecht
Ufliand IaS (1967) Integral transforms in the theory of elasticity. Second edition: Nauka, Leningrad, English translation of the first edition: Survey of articles on the application of integral transforms in the theory of elasticity. North Carolina State University (1965), Applied Mathematics Research Group, File No. PSR-24/6
Fabrikant VI (2005) Tangential contact problem for a transversely isotropic elastic layer bonded to a rigid foundation. Proc Camb Soc 138: 173–191
Fabrikant VI (2011) Tangential contact problem for a transversely isotropic elastic layer bonded to an elastic foundation. J Eng Math 70:363–388
Fabrikant VI (2011) Numerical methods of solution of contact problems in layered media. Int J Comput Methods Eng Sci Mech 12(2): 84–95
Fabrikant VI (1997) Generalized method of images in the crack analysis. Int J Eng Sci 35: 1159–1184
Gradshteyn IS, Ryzhik IM (1994) Tables of integrals, series and products. Academic Press, New York
Fabrikant VI (2010) Contact and crack problems in linear theory of elasticity. Bentham Science Publishing, Sharjah
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fabrikant, V.I. Tangential contact problems for several transversely isotropic elastic layers bonded to an elastic foundation. J Eng Math 81, 93–126 (2013). https://doi.org/10.1007/s10665-012-9546-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10665-012-9546-0