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IssuesArchive of Issues2006-3pp.81-92

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P. P. Krasnyuk, "Ring-cylinder thermoelastic contact interaction with nonstatinary frictional heat generation," Mech. Solids. 41 (3), 81-92 (2006)
Year 2006 Volume 41 Number 3 Pages 81-92
Title Ring-cylinder thermoelastic contact interaction with nonstatinary frictional heat generation
Author(s) P. P. Krasnyuk (Lvov)
Abstract Contact joints consisting of elastic cylinders compressed by ring-shaped bands are widely used in machine design, which makes it topical to study the corresponding contact problems. Although a fairly thorough analysis of the interaction of an elastic cylinder with a rigid band was performed in [1], the contact of elastic bodies still remains a problem to be studied. What makes this task especially difficult is the absence of exact analytical solutions of differential equations of thermoelasticity for finite bodies. For this reason, in many investigations the contact model is based on generalizations of the classical approach proposed by Hertz. In particular, the interaction of a long cylinder with an elastic band was considered in [2] under the assumption that the radial displacement of the band can be approximated by the displacements depending on the same force factors as those arising in the problem of a long cylindrical pit in an elastic space. Thereby, the problem was reduced to an integral equation for the contact pressure.

Another approach involves the averaging of boundary conditions over the contact area, which makes it possible to find the main trends in the behavior of tribosystems under consideration and, in many cases, obtain approximate analytical formulas for a class of problems the exact solution of which is extremely difficult from the analytical and computational standpoints. This method was fully utilized in [3], where the case of a long cylinder compressed by a thin elastic ring was analyzed and an analytical formula was obtained for contact pressure.

The approach of [3] is applied here to a new thermoelasticity problem of interaction between a hollow cylinder embraced, without pre-tension, by a ring-shaped plate of constant thickness with nonstationary heat generation due to friction forces in the contact region. This problem is reduced to a system of integral equations, and an effective method is proposed for its solution. In the special case of stationary heat generation, an analytical formula is obtained for the contact pressure.
References
1.  V. M. Alexandrov, "An axisymmetric contact problem for an infinite elastic cylinder," Izv. AN SSSR, OTN. Mekh. i Mashinostr., No. 5, pp. 91-94, 1962.
2.  V. M. Alexandrov and B. L. Romalis, Contact Problems in Engineering [in Russian], Mashinostroenie, Moscow, 1986.
3.  N. Kh. Arutyunian, "On the contact interaction of an elastic ring and an elastic cylinder," Izv. RAN, MTT [Mechanics of Solids], No. 2, pp. 204-206, 1994.
4.  Ya. S. Podstrigach and Yu. M. Kolyano, Transient Temperature Fields and Stresses in Thin Plates [in Russian], Naukova Dumka, Kiev, 1972.
5.  G. Korn and T. Korn, Handbook on Mathematics for Researchers and Engineers [Russian translation], Nauka, Moscow, 1977.
6.  D. V. Grilitskii and P. P. Krasnyuk, "Quasistatic contact interaction of two ring-shaped plates with heat generation due to friction," Dokl. NAN Ukr., No. 1, pp. 41-45, 1995.
7.  D. V. Grilitskii and P. P. Krasnyuk, "Thermoelastic contact of two cylinders with nonstationary heat generation due to friction," PMTF, Vol. 38, No. 3, pp. 112-121, 1997.
8.  A Handbook on Special Funbctions with Formulas, Graphs, and Mathematical Tables [Russian translation], Ed. by M. Abramovitz and I. Stigan, Nauka, Moscow, 1979.
Received 17 December 2003
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