 | | 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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| K. I. Romanov, "Energy method in the theory of buckling of rheonomic rods," Mech. Solids. 39 (3), 101-108 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
3 |
Pages |
101-108 |
| Title |
Energy method in the theory of buckling of rheonomic rods |
| Author(s) |
K. I. Romanov (Moscow) |
| Abstract |
Unlike the theory of stability of a rectilinear shape of equilibrium [1], the theory of buckling of rods is characterized by the existence of a small initial imperfection in the form of a distortion of the axis. The energy method for the determination of the critical time was suggested in [2] for the buckling problems for rods loaded by concentrated forces at the ends in the creep conditions. In what follows, this method is generalized to the case of an arbitrary system of forces including distributed loads.
It is proved that the proposed energy method gives an upper estimate of the real critical time. A similarity between the basic equation of the energy method and the relaxation equation of the rheonomic model for a rod subjected to tension or compression is established. A new relation is obtained defining the increase of deflections with time, depending on the exponent in the equation of state for a nonlinear viscous material.
As an example, the critical time is determined in the buckling problem for a rod loaded by the pressure uniformly distributed over the length of the rod. This pressure can be caused by the gravitational field. In this case, the theoretical solution obtained is of interest for problems of design of towers and other tall structures when predicting the no-failure operation time. |
| References |
| 1. | Yu. N. Rabotnov and S. A. Shesterikov, "Stability of rods and plates in creep conditions," PMM [Applied Mathematics and Mechanics], Vol. 21, No. 3,
pp. 406-412, 1957. |
| 2. | K. I. Romanov, "Longitudinal bending of nonlinearly viscous rods,"
Raschety na Prochnost, No. 3, pp. 139-151, 1993. |
| 3. | L. M. Kachanov, Theory of Creep [in Russian], Fizmatgiz, Moscow, 1960. |
| 4. | K. I. Romanov, "Investigation of the creep buckling of a rod on the basis of the Calladine-Drucker theorem," Izv. AN. MTT [Mechanics of Solids],
No. 4, pp. 157-161, 1999. |
| 5. | E. S. Lazarenko, N. N. Malinin, and K. I. Romanov, "A method of evaluation of the stress relaxation in the conditions of hot forming of metals and its application for interindustrial standardization," in S. A. Shesterikov (Editor), Unified Methods for Creep and Long-Term Strength Analysis [in Russian], No. 7, pp. 16-21, Izd-vo Standartov, Moscow, 1986. |
| 6. | K. I. Romanov, Mechanics of Hot Forming of Metals [in Russian], Mashinostroenie, Moscow, 1993. |
| 7. | N. N. Malinin, Applied Theory of Plasticity and Creep [in Russian], Mashinostroenie, Moscow, 1975. |
| 8. | A. A. Il'yushin, Plasticity [in Russian], Gostekhizdat, Leningrad, Moscow, 1948. |
|
| Received |
02 April 2002 |
| << Previous article | Volume 39, Issue 3 / 2004 | Next article >> |
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