 | | 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
|
| In English (Mech. Solids): | | 4810 |
|
| << Previous article | Volume 40, Issue 2 / 2005 | Next article >> |
| K. I. Romanov, "The shapes of a rheonomic bar in a gravity field," Mech. Solids. 40 (2), 113-120 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
2 |
Pages |
113-120 |
| Title |
The shapes of a rheonomic bar in a gravity field |
| Author(s) |
K. I. Romanov (Moscow) |
| Abstract |
On the basis of the hypothesis of plane sections, a new solution is
obtained for the problem of relating the Lagrange and Euler coordinates in
the creep of a bar stretched by the forces of its own weight. A version of
the method of successive approximations is proposed. It is shown that the
homogeneous strain state can be adopted as the initial approximation which
ensures the convergence of the successive approximations. As a result, the
time dependence of the bar shape is determined and the fracture time is
obtained in accordance with the Hoff scheme corresponding to infinite
elongation. The bar shape is studied for large creep strains as a function
of the exponent in the constitutive relation for a nonlinearly viscous
body.
Two different problems of the bar shape are solved, namely, the direct
one, in which the current shape at an arbitrary instant of time is
determined for a given initial shape, and the inverse one, in which the
lateral bar surface at the initial instant of time is determined for the
shape given at a certain instant. The solutions can be applied to the
design of new technologies of making elongated crystals and nibs of
complicated shapes formed due to a natural source of geomechanical energy. |
| References |
| 1. | P. F. Papkovich, Theory of Elasticity [in Russian], Oborongiz,
Moscow, 1939. |
| 2. | Yu. N. Rabotnov, Creep of Structural Members [in Russian], Nauka,
Moscow, 1966. |
| 3. | Rayleigh Lord, The Theory of Sound, MacMillan, Liverpool, 1929. |
| 4. | V. F. Zaytsev and A. D. Polyanin, Handbook on Nonlinear Ordinary
Differential Equations [in Russian], Factorial, Moscow, 1977. |
| 5. | E. Kamke, Handbook on Ordinary Differential Equations [Russian
translation], Izd-vo Inostr. Lit-ry, Moscow, 1950. |
|
| Received |
08 April 2003 |
| << Previous article | Volume 40, Issue 2 / 2005 | Next article >> |
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