 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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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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