 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| I. V. Andrianov and O. G. Samoilenko, "On the Ishlinskii-Leibenzon method in the theory of elastic stability," Mech. Solids. 36 (6), 113-119 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
6 |
Pages |
113-119 |
| Title |
On the Ishlinskii-Leibenzon method in the theory of elastic stability |
| Author(s) |
I. V. Andrianov (Dnepropetrovsk)
O. G. Samoilenko (Dnepropetrovsk) |
| Abstract |
A. Yu. Ishlinskii [1] and L. S. Leibenzon [2] suggested a method for the
stability analysis of elastic systems applicable to structures with free
edges (or solids with free surfaces). The essence of this method
is that the parametric terms are neglected in the stability equations, but
are preserved only in the boundary conditions. This method has become widely
used [3-10] (see also the list of bibliography in [11-15]) and has been
repeatedly discussed in the literature [13-15]; a number of reasonable
critical remarks have been stated as regards the accuracy of this method.
For example, in [13], it is mentioned that "numerous publications based on
the approximate method of [1, 2] need an additional study to define the
limits of their applicability."
In the present paper we show that these remarks can be removed by regarding
this approach as a zeroth-order approximation of an asymptotic process
admitting refinement. |
| References |
| 1. | A. Yu. Ishlinskii, "Considering the stability of equilibrium
of elastic bodies from the point of view of the mathematical theory of
elasticity," Ukrainskii Matematicheskii Zhurnal, Vol. 6, No. 2,
pp. 140-146, 1954. |
| 2. | L. S. Leibenzon, "On the application of harmonic functions to the
stability of spherical and cylindrical shells," in L. S. Leibenzon,
Collected Works [in Russian], Vol. 1, pp. 50-86, Izd-vo AN SSSR, Moscow,
1951. |
| 3. | M. T. Alimzhanov, Stability of Equilibrium of Solids and Problems
of Mechanics of Rocks [in Russian], Nauka, Alma-Ata, 1982. |
| 4. | L. V. Ershov, "On the statement of the problems for stability of
mining shafts," Doklady AN SSSR, Vol. 143, No. 2, pp. 305-307, 1962. |
| 5. | N. F. Voitsekhovskaya, "A stability of cylindrical shells from the
point of view of the mathematical theory of elasticity," Doklady AN SSSR,
Vol. 266, No. 1, pp. 59-63, 1982. |
| 6. | L. V. Ershov and D. D. Ivlev, "On the buckling of a thick-walled
pipe under internal pressure," Izv. AN SSSR. OTN, No. 8, pp. 149-152,
1957. |
| 7. | I. D. Legenya, "On the stability of thick rectangular simply
supported plate under compressive loads," Doklady AN SSSR, Vol. 140,
No. 4, pp. 776-779, 1961. |
| 8. | Zh. S. Erzhanov and A. K. Egorov, Theory of Folding Process
in Rock Mass (Mathematical Description) [in Russian], Nauka, Alma-Ata, 1968. |
| 9. | Zh. S. Erzhanov, A. K. Egorov, I. A. Garagash et al. (Editors)
Theory of Folding in the Earth's Crust [in Russian], Nauka, Moscow, 1975. |
| 10. | O. V. Gendelman and L. I. Manevitch, "Local buckling of reinforced
cylindrical shells," in VII Sympozjum Statecznosci Konstrukcji, pp. 27-31,
Bielsko-Biala, 1994. |
| 11. | A. N. Guz', Stability of Three-dimensional Solids
[in Russian], Naukova dumka, Kiev, 1971. |
| 12. | A. N. Guz' and A. N. Skorykhin, "Three-dimensional theory of
inelastic stability," Prikladnaya Mekhanika, Vol. 18, No. 7, pp. 3-22,
No. 8, pp. 3-27, 1982. |
| 13. | A. N. Guz', "On the three-dimensional theory of stability of
deformable solids. Internal instability," Prikladnaya Mekhanika, Vol. 21,
No. 11, pp. 3-17, 1985. |
| 14. | A. N. Guz', "On the three-dimensional theory of stability of
deformable solids. Surface stability," Prikladnaya Mekhanika, Vol. 22,
No. 1, pp. 24-35, 1986. |
| 15. | A. N. Guz', "On the three-dimensional theory of stability of
deferrable solids. Stability of structural components," Prikladnaya
Mekhanika, Vol. 22, No. 2, pp. 3-17, 1986. |
| 16. | V. L. Berdichevskii, "A variational asymptotic method for
constructing the theory of shells," PMM [Applied Mathematics and
Mechanics], Vol. 43, No. 4, pp. 664-687, 1979. |
| 17. | V. L. Berdichevskii, Variational Principles in Mechanics of a
Continuous Medium [in Russian], Nauka, Moscow, 1983. |
| 18. | N. A. Alfutov, Fundamentals of Stability Analysis of Elastic
Systems [in Russian], Mashinostroenie, Moscow, 1978. |
| 19. | I. F. Obraztsov, B. V. Nerubailo, and I. V. Andrianov, Asymptotic
Methods in Mechanics of Thin-walled Structures [in Russian],
Mashinostroenie, Moscow, 1991. |
| 20. | J. Baker and P. Graves-Morris, Padé Approximations [Russian
translation], Mir, Moscow, 1982. |
| 21. | I. L. Birger and Ya. G. Panovko (Editors), Strength, Stability,
and Vibrations. Volume 3 [in Russian], Mashinostroenie, Moscow, 1968. |
| 22. | D. V. Vainberg and E. D.Vainberg, Plates, Disks, and Thin-walled
Beams (Strength, Stability, and Vibrations) [in Russian], Gosstroiizdat
UkrSSR, Kiev, 1959. |
|
| Received |
02 June 1997 |
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