 | | 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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| M.Ya. Brovman, "On the Choice of Coordinates in the Analysis of Plane Plastic Strain," Mech. Solids. 46 (3), 357-367 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
3 |
Pages |
357-367 |
| DOI |
10.3103/S0025654411030034 |
| Title |
On the Choice of Coordinates in the Analysis of Plane Plastic Strain |
| Author(s) |
M.Ya. Brovman ("Module-Engineering" LTD, Sadovnicheskaya 20-1, Moscow, 115035 Russia, brovman@mail.ru) |
| Abstract |
The plane strain of an ideal rigid-plastic medium is studied
in curvilinear coordinates. The methods used to solve the equations of plasticity were considered in [1-3].
Curvilinear orthogonal coordinates with the introduction of a metric function were used in [4, 5].
In the present paper, specific features of the choice of a
coordinate system in which the coordinate lines are the slip lines or the principal stress lines are studied and solutions containing coordinate functions determined by the metric tensor for the two-dimensional space are obtained. |
| Keywords |
plastic strain, curvilinear coordinates, equilibrium equations |
| References |
| 1. | V. V. Sokolovskii,
The Theory of Plasticity
(Vysshaya Shkola, Moscow, 1969)
[in Russian]. |
| 2. | D. D. Ivlev,
Theory of Perfect Plasticity
(Nauka, Moscow, 1966)
[in Russian]. |
| 3. | R. Hill,
The Mathematical Theory of Plasticity
(Clarendon press, Oxford, 1950; Gostekhizdat, Moscow, 1956). |
| 4. | M. Ya. Brovman,
"Solution of Equations of a Plastic Flow in Curvilinear Coordinates,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 86-97 (2004)
[Mech. Solids (Engl. Transl.)
39 (4), 68-76 (2004)]. |
| 5. | M. Ya. Brovman,
"Solution of the Plastic Flow Equations under Axisymmetric Deformation,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 137-146 (2007)
[Mech. Solids (Engl. Transl.)
42 (2), 283-290 (2007)]. |
| 6. | L. I. Golovina,
Linear Algebra and Some Applications
(Nauka, Moscow, 1971)
[in Russian]. |
| 7. | M. Ya. Brovman,
Application of the Theory of Plasticity in Rolling
(Metallurgiya, Moscow, 1991)
[in Russian]. |
|
| Received |
15 October 2008 |
| Link to Fulltext |
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