 | | 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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| 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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