 | | 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, "Transverse-longitudinal bending of rheonomic rods," Mech. Solids. 42 (1), 135-139 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
1 |
Pages |
135-139 |
| Title |
Transverse-longitudinal bending of rheonomic rods |
| Author(s) |
K. I. Romanov (Bauman Moscow State Technical University, 2-ya Baumanskaya 5, Moscow, 105005, Russia) |
| Abstract |
In [1, 2], an energy method for the determination of critical buckling times is developed for rods subjected to compression in the conditions of longitudinal bending. In this case, for given compressive loads, the bending moments in the rod cross-sections depend only on the current deflection of the rod axis.
In contrast to longitudinal bending, in the case of transverse-longitudinal bending the bending moment in general depends not only on the deflection but also on the axial coordinate and the reaction forces in the supports. Depending on the rod fixing conditions, the problems of transverse-longitudinal bending can be categorized as statically determinate or statically indeterminate. In the latter case, the derivation of equilibrium conditions for a rod segment is complicated by the indefiniteness of the reactions in the rod buckling process.
In the current paper, the energy method developed in [1, 2] is extended to a class of statically indeterminate transverse-longitudinal bending problems. To determine the redundant variables, it is proposed to use the principle of minimum of additional dissipation. |
| References |
| 1. | K. I. Romanov, "Buckling of Nonlinearly Viscous Rods," in
Strength Design
(Mashinostroenie, Moscow, 1993),
Vol. 33, pp. 139-151. |
| 2. | K. I. Romanov,
"Energy Method in the Buckling Theory of Rheonomic Rods,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 125-134 (2004)
[Mech. Solids (Engl. Transl.)]. |
| 3. | L. M. Kachanov,
Theory of Creep
(Fizmatgiz, Moscow, 1960)
[in Russian]. |
| 4. | E. T. Whittaker and G. N. Watson,
A Course of Modern Analysis
(Univ. Press, Cambridge, 1927; Editorial URSS, Moscow, 2002). |
|
| Received |
08 July 2004 |
| Link to Fulltext |
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