 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| D. V. Georgievskii and B. E. Pobedrya, "On the concept of stability of deformation in elastic and viscoelastic models," Mech. Solids. 37 (4), 37-46 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
4 |
Pages |
37-46 |
| Title |
On the concept of stability of deformation in elastic and viscoelastic models |
| Author(s) |
D. V. Georgievskii (Moscow)
B. E. Pobedrya (Moscow) |
| Abstract |
Numerous attempts have been made to provide the concept of stability
with a rigorous mathematical definition allowing one to construct
a mathematical model of the transition of a motion or an equilibrium
(more generally, a process) from a stable state to an unstable one.
Most of the attempts to propose a unified definition failed, since
in each specific problem the physical meaning implied a specific
interpretation of the term stability. For example,
in statics of structures this term means the ability of the system
to preserve equilibrium under the action of certain loads. In problems
of dynamics and vibrations of rigid bodies, stability means that
the perturbed motion deviates from the unperturbed one by no more
than a certain quantity. In hydrodynamics, the stability is usually
interpreted as the property of the flow to remain laminar. Accordingly,
the loss of stability means the transition to a turbulent regime.
One should also refer to this concept when considering the change
of the internal structure of solids on micro, meso, and macro levels
and nucleation of phase transitions [1]. |
| References |
| 1. | N. F. Morozov and A. B. Freidin, "Phase transition zones and phase
transformations for various kinds of stress state," in Transactions
of the Mathematical Institute of the Russian Academy of Sciences [in Russian],
Vol. 223, pp. 220-232, 1998. |
| 2. | T. Poston and I. Stewart, Catastrophe Theory and Its
Applications [Russian translation], Mir, Moscow, 1980. |
| 3. | N. G. Chetaev, Stability of Motion [in Russian], Nauka, Moscow, 1965. |
| 4. | S. P. Timoshenko, Stability of Rods, Plates, and Shells
[Russian translation], Nauka, Moscow, 1971. |
| 5. | N. A. Alfutov, Fundamentals of the Stability Analysis
of Elastic Systems [in Russian], Mashinostroenie, Moscow, 1991. |
| 6. | V. V. Bolotin, Non-conservative Problems of the Theory
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| 9. | B. E. Pobedrya and D. V. Georgievskii, Lectures on the Theory
of Elasticity [in Russian], Editorial URSS, Moscow, 1999. |
| 10. | D. V. Georgievskii, "Stability of deformation processes
with respect to sets of measures for given classes of perturbations,"
Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 69-92, 1997. |
| 11. | A. R. Rzhanitsyn, Some Issues of Mechanics of Systems
Subject to Time-varying Deformation [in Russian],
Gostekhizdat, Moscow, 1949. |
| 12. | Yu. N. Rabotnov, Creep in Structural Members [in Russian],
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| 13. | L. M. Kurshin, "Creep stability,"
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| 14. | R. S. Sanzharovskii, Creep Stability of Structural Elements of
Buildings [in Russian], Izd-vo LGU, Leningrad, 1984. |
| 15. | V. D. Potapov, Stability of Viscoelastic Structural
Members [in Russian], Stroiizdat, Moscow, 1985. |
| 16. | N. Kh. Arutyunyan, A. D. Drozdov, and V. B. Kolmanivskii,
"Stability of Viscoelastic Bodies and Structural Members,"
in Achievements in Science and Technology. Ser. Mechanics
of Solids [in Russian], Vol. 19, pp. 3-77, VINITI, Moscow, 1987. |
| 17. | A. A. Il'yushin and B. E. Pobedrya, Mathematical Fundamentals
of the Theory of Thermoviscoelasticity [in Russian], Nauka, Moscow, 1971. |
| 18. | K. A. Abgaryan, "Stability of motion on a finite time interval,"
in Achievements in Science and Technology. Ser. General Mechanics
[in Russian], Vol. 3, pp. 43-124, VINITI, Moscow, 1976. |
| 19. | S. A. Shesterikov, "On the criterion of the creep stability,"
PMM [Applied Mathematics and Mechanics], Vol. 23, No. 6, pp. 1101-1106,
1959. |
| 20. | N. J. Hoff, "Reversed creep: a remark to the creep buckling
theory of Rabotnov and Shesterikov," J. Mech. Phys. Solids, Vol. 12,
No. 2, pp. 113-125, 1964. |
| 21. | I. G. Treuglov, Bending and Creep Buckling of Thin Plates
and Shells [in Russian], Nauka, Moscow, 1969. |
| 22. | A. N. Guz', "On a model in the 3D theory of stability
of elastoviscoplastic bodies,"
Prikladnaya Mekhanika, Vol. 20, No. 6, pp. 18-24, 1984. |
| 23. | V. D. Klyushnikov, Lectures on Stability of Deformable
Systems [in Russian], Izd-vo MGU, Moscow, 1986. |
| 24. | V. G. Zubchaninov, O. E. Sof'in, and S. L. Subbotin,
"Stability and buckling of nonlinearly elastic compressed rods
subject to creep," in Stability, Plasticity, and Creep under
Complex Loading [in Russian], pp. 76-87, Izd-vo Tver. GTU, Tver, 1998. |
| 25. | V. G. Gromov, "Quasistatic instability as a means for
the qualitative analysis of equilibrium motions of hereditarily deformed
bodies on a finite time interval,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 5, pp. 124-127, 1986. |
|
| Received |
30 April 2002 |
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