 | | 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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| K. I. Romanov, "Static statement of the stability problem under creep," Mech. Solids. 43 (2), 277-282 (2008) |
| Year |
2008 |
Volume |
43 |
Number |
2 |
Pages |
277-282 |
| DOI |
10.3103/S0025654408020143 |
| Title |
Static statement of the stability problem under creep |
| Author(s) |
K. I. Romanov (Bauman Moscow State Technical University, 2-ya Baumanskaya 5, Moscow, 105005, Russia) |
| Abstract |
In technological processes of rod bending, the critical time is determined [1] by the criterion of unbounded increase A →∞ in the bent axis amplitude, which is equivalent to the requirement A »A0, where A0 is value of the amplitude at the initial time t=0. In this case, the mathematical models of the process of buckling of rods and plates [2] are constructed in the framework of the theory of small displacements. This contradiction can be removed by the assumption that the critical state is realized for deflections A of the order of several A0, i.e., at the time instant corresponding to a sharp increase in displacements. Naturally, this assumption is of local character, because the instant of the transition to the accelerated increase in deflections depends on specific conditions such as, for example, the support conditions, the creep coefficient, the type of the system imperfectness, the value of A0, and the eccentricity of the load application.
In what follows, we show that, in the case of longitudinal bending (buckling), the time instant directly preceding the beginning of the catastrophic increase in deflections can be determined by the variation in the phase volume of the system. |
| References |
| 1. | K. I. Romanov,
"Energy Method in the Theory of Buckling of Rheonomic Rods,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 125-134 (2004)
[Mech. Solids (Engl. Transl.)
39 (3), 101-108 (2004)]. |
| 2. | K. I. Romanov,
"Critical Time in the Theory of Buckling of Plates Subject to Creep,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 114-120 (2004)
[Mech. Solids (Engl. Transl.)
39 (5), 91-96 (2004)]. |
| 3. | J. W. Gibbs,
Elementary Principles of Statistical Mechanics
(Ox Bow Press, Woodbridge, CT, 1981; SPC. "Regular & Chaotic Dynamics," Moscow-Izhevsk, 2002). |
| 4. | S. V. Vallander,
Lecture in Hydroaeromechanics
(Izd. LGU, Leningrad, 1978)
[in Russian]. |
| 5. | K. I. Romanov,
"Buckling of Nonlinearly Viscous Rods,"
in Strength Design
(Mashinostroenie, Moscow, 1993),
Vol. 33, pp. 139-151
[in Russian]. |
| 6. | A. Yu. Loskutov and A. S. Mikhailov,
Introduction to Synergy
(Nauka, Moscow, 1990)
[in Russian]. |
| 7. | E. N. Moshnin,
Bending and Straightening on Rotation Machines
(Mashinostroenie, Moscow, 1967)
[in Russian]. |
| 8. | N. N. Malinin,
Applied Theory of Plasticity and Creep
(Mashinostroenie, Moscow, 1975)
[in Russian]. |
| 9. | A. A. Andronov, A. A. Vitt, and S. E. Khaikin,
Theory of Oscillators
(Fizmatgiz, Moscow, 1959; Pergamon, London, 1966). |
| 10. | V. I. Arnold,
Catastrophe Theory
(Springer-Verlag, Berlin, 1992; Editorial URSS, Moscow, 2004). |
| 11. | M. I. Rabinovich and D. I. Trubetskov,
Introduction to the Theory of Oscillations and Waves
(SPC. "Regular & Chaotic Dynamics," Moscow-Izhevsk, 2000)
[in Russian]. |
| 12. | D. C. Drucker,
"On the Postulate of Stability of Material in Mechanics of Continua,"
in Proc. of 2nd All-Union Congress in Theoretical
and Applied Mechanics, Moscow, 1964,
Mechanics. Collection of Translations of Foreign Papers
(Moscow, 1964),
No. 3, pp. 115-128. |
| 13. | L. M. Kurshin,
"On the Statement of Stability Problem under Creep Conditions,"
in Problems of Theory of Plasticity and Creeping
(Mir, Moscow, 1979),
pp. 246-302
[in Russian]. |
|
| Received |
07 February 2005 |
| Link to Fulltext |
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