 | | 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, "Critical time in the theory of buckling of plates subject to creep," Mech. Solids. 39 (5), 91-96 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
5 |
Pages |
91-96 |
| Title |
Critical time in the theory of buckling of plates subject to creep |
| Author(s) |
K. I. Romanov (Moscow) |
| Abstract |
A theory of buckling of plates subject to creep was developed in [1, 2]. This theory enables one to determine approximately the critical time that corresponds to the catastrophic increase in the deflection. The form of the basic differential equation depends on the shape of the contour of the plate. This equation is integrated in accordance with the Bubnov-Galerkin-Kantorovich method. We utilized the polar coordinates in the case of axially symmetric buckling [1] and the Cartesian coordinates in the case of buckling of rectangular plates [2].
In the present paper, we estimate the accuracy of the approximate scheme proposed for solving problems of plate buckling for the case of an extended rectangular plate. It is indicated, in addition, that the critical time t* is a physical invariant and, hence, cannot depend on the choice of the coordinate system. Accordingly, the critical time can be calculated on the basis of a unified basic differential equation. This equation, for example, can be written for the deflection function subjected to the boundary conditions for the plate with an arbitrary curvilinear contour and represented in the Cartesian coordinates. |
| References |
| 1. | K. I. Romanov, "Analysis of buckling of a circular plate subject to creep,"
Vestnik MGTU, Ser. Mashinostroenie, No. 4, pp. 91-97, 1995. |
| 2. | K. I. Romanov, "Analysis of buckling of a rectangular plate subject to creep,"
Vestnik MGTU, Ser. Mashinostroenie, No. 3, pp. 109-116, 1995. |
| 3. | K. I. Romanov, "Buckling of nonlinearly viscous rods,"
in Strength Analysis [in Russian], No. 33, pp. 139-151, Mashinostroenie, Moscow, 1993. |
| 4. | C. R. Calladine and D. C. Drucker, "Nesting surfaces of constant rate of energy dissipation in creep,"
Qart. Appl. Math., Vol. 20, No. 1, pp. 79-84, 1962. |
| 5. | K. I. Romanov, "Analysis of buckling of a rod subject to creep on the basis of the Calladine-Drucker theorem,"
Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 157-161, 1999. |
| 6. | S. D. Ponomarev, V. L. Biderman, K. K. Likharev, et al.,
Strength Analysis in Mechanical Engineering. Volume 2: Some Problems of Applied Theory of Elasticity
[in Russian], Mashgiz, Moscow, 1958. |
| 7. | O. V. Aminov and K. I. Romanov,
"Plane stress state of an annular plate
subject to creep under large deformation,"
Vestnik MGTU, Ser. Mashinostroenie, No. 2, pp. 104-114, 1999. |
| 8. | S. V. Boyarshinov,
Fundamentals of Structural Mechanics of Machines
[in Russian],
Mashinostroenie, Moscow, 1973. |
| 9. | B. G. Galerkin, Collected Works. Volume 2 [in Russian],
Izd-vo AN SSSR, Moscow, 1953. |
| 10. | Ya. S. Uflyand, Bipolar Coordinates in Elasticity
[in Russian], Gostekhizdat, Moscow, Leningrad, 1950. |
|
| Received |
19 September 2002 |
| << Previous article | Volume 39, Issue 5 / 2004 | Next article >> |
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