Summary
This paper deals with the contact problem of a rigid cylinder pressed on an elastic layer connected rigidly to a rigid base. It is assumed that there is no friction between cylinder and layer and that the cylinder is long enough to ensure a plane deformation. Asymptotic solutions are presented when the ratio of the half width c of the contact area to the thickness b of the layer is small and also when c/b is large. The breakdown of the asymptotic solution for large values of c/b when the material is incompressible, discussed by Koiter [6], is overcome by considering a more general solution of the Wiener-Hopf integral equation encountered. The results of both asymptotic solutions match so well that a satisfactory solution is obtained for all values c/b and for 0≦ν≦0.5.
Similar content being viewed by others
References
Aleksandrov, V. M., Prikl. Mat. Mekh. 26 (1962) 1410 (in English translation).
Aleksandrov, V. M., Prikl. Mat. Mekh. 27 (1963) 1490 (in English translation).
Aleksandrov, V. M. and I. I. Vorovich, Prikl. Mat. Mekh. 28 (1964) 425 (in English translation).
Hannah, M., Quart. J. Mech. Appl. Maths., IV (1951) 94.
Koiter, W. T., Proc. Kon. Ned. Ak. Wet., Amsterdam, B 57 (1954) 558.
Koiter, W. T., Solution of some elasticity problems by asymptotic methods, Proc. of the International Symposium, Tbilisi September 1963.
Miller, R. D. W., Appl. Sci. Res. 16 (1966) 405.
Muskhelishvili, N. I., Singular integral equations, P. Noordhoff N.V., Groningen 1953 (translation from Russian second edition).
Noble, B., Methods based on the Wiener-Hopf technique for the solution of partial differential equations, Pergamon Press, London 1958.
Sparenberg, J. A., Proc. Kon. Ned. Ak. Wet., Amsterdam, A 59 (1956) 29.
Titchmarsh, E. C., Introduction to the theory of Fourier integrals, second edition, Clarendon Press, Oxford 1948.
Tricomi, F. G., Integral equations, Interscience Publishers Inc., New York 1957.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Meijers, P. The contact problem of a rigid cylinder on an elastic layer. Appl. Sci. Res. 18, 353–383 (1968). https://doi.org/10.1007/BF00382359
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00382359