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IssuesArchive of Issues2001-4pp.94-101

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G. G. Zorina, P. G. Pimshtein, and L. B. Tsvik, "On an elastic annulus compressed by two diametrically opposite forces," Mech. Solids. 36 (4), 94-101 (2001)
Year 2001 Volume 36 Number 4 Pages 94-101
Title On an elastic annulus compressed by two diametrically opposite forces
Author(s) G. G. Zorina (Irkutsk)
P. G. Pimshtein (Irkutsk)
L. B. Tsvik (Irkutsk)
Abstract The problem of elasticity for a homogeneous isotropic annulus subjected to compression is solved on the basis of S. P. Timoshenko's approach [1] which uses the solution of a similar problem for a disk. The solution obtained is effective for various values of the parameter β=r2/r1, where r1 and r2 are the inner and outer radii of the annulus, respectively. This solution is expressed by the series the general term of which is obtained in closed form. The solution is used to evaluate the error of approximate solutions constructed by using the finite element method (FEM) and to assess the applicability area of the approximate solution obtained in the theory of thin annuli. The distribution of the radial stresses in a continuous ring is used to analyze the character of delamination in a two-layered annulus subjected to compression, the layers of which are smooth, have the same thickness, and contact without preload. It is established that for large values of β, two zones of delamination appear, the centers of which lie on the line perpendicular to the line of application of the external forces. For small values of β, four zones of delamination appear that approach the line of application of the forces as β decreases.
References
1.  S. P. Timoshenko, Strength and Vibration of Structural Elements [Russian translation], Nauka, Moscow, 1975.
2.  P. F. Papkovich, Theory of Elasticity [in Russian], Oborongiz, Leningrad, Moscow, 1939.
3.  Yu. A. Ustinov, "Calculation of stresses in a circular annulus," Izv. AN SSSR. Mekhanika i Mashinostroenie, No. 1, pp. 33-45, 1964.
4.  I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Fizmatgiz, Moscow, 1962.
5.  A. I. Lur'e, Theory of Elasticity [in Russian], Nauka, Moscow, 1970.
6.  L. B. Tsvik, Application of the Finite Element Method to Statics of Deformation [in Russian], Izd-vo IGU, Irkutsk, 1995.
7.  G. I. Marchuk, Methods of Computational Mathematics [in Russian], Nauka, Moscow, 1989.
8.  I. A. Birger, B. F. Shorr, and G. B. Iosilevich, Strength Analysis of Machine Components. Handbook [in Russian], Mashinostroenie, Moscow, 1979.
9.  A. Love, A Treatise on the Mathematical Theory of Elasticity [Russian translation], ONTI, Moscow, Leningrad, 1935.
10.  L. B. Tsvik, "On the residuals of matching the stresses and displacements in problems of matching and contact of elastic bodies," Doklady AN SSSR, Vol. 268, No. 3, pp. 570-574, 1983.
11.  L. B. Tsvik, P. G. Pimshtein, and G. G. Zorina, "On the influence function for an elastic annulus," Doklady AN, Vol. 366, No. 5, pp. 636-638, 1999.
Received 04 February 1999
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