 | | 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: | | 13554 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8194
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| In English (Mech. Solids): | | 5360 |
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| << Previous article | Volume 60, Issue 7 / 2025 | Next article >> |
| Y.N. Radayev, "On the Canonical Forms of Self-Similar Equations in the Axisymmetric Problem of Plasticity Theory," Mech. Solids. 60 (7), 6577-6582 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
7 |
Pages |
6577-6582 |
| DOI |
10.1134/S0025654425606925 |
| Title |
On the Canonical Forms of Self-Similar Equations in the Axisymmetric Problem of Plasticity Theory |
| Author(s) |
Y.N. Radayev (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, radayev@ipmnet.ru, y.radayev@gmail.com) |
| Abstract |
This paper is dedicated to the equations obtained through a self-similar transformation of
variables under axisymmetric conditions from the general three-dimensional equations of the mathematical theory of plasticity with the Tresca yield condition and the associated flow rule for the stress
states corresponding to an edge of the yield surface. It has been shown that some self-similar solutions
can be derived from a single ordinary differential equation involving a root-type irrational term on the
right-hand side. Proper substitutions transform this equation to an irrationality-free form, which is
classified as the Abel equation of the first kind, that makes it possible to represent its integrals by applying the results of the analytical theory of differential equations. |
| Received |
13 September 2025 | Revised |
20 September 2025 | Accepted |
13 October 2025 |
| Link to Fulltext |
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