 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| Yu. N. Bakhareva and Yu. N. Radaev, "A generalization of Shield's self-similar solutions of the axially symmetric problem of plasticity," Mech. Solids. 40 (2), 86-96 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
2 |
Pages |
86-96 |
| Title |
A generalization of Shield's self-similar solutions of the axially symmetric problem of plasticity |
| Author(s) |
Yu. N. Bakhareva (Samara)
Yu. N. Radaev (Samara) |
| Abstract |
A generalization of self-similar solutions of the axially symmetric problem
that correspond to the yield on a Tresca prism edge is considered. These
solutions have been obtained by Shield [1]. The search for new self-similar
solutions is based on the relationships of the spatial problem represented
in the isostatic coordinates, with the axial symmetry and the possibility
of the separation of an additional non-angular coordinate being taken
into account. It is established that the axially symmetric problem
of plasticity has a number of self-similar solutions in which the products
of powers of the isostatic coordinates play the role of self-similar
variables. For some specific values of the exponents occurring in the representation
of a self-similar solution, the order of the equations of the axially
symmetric problem can be reduced by one and the problem can thus be reduced
to one nonlinear time-varying first-order equation which then can be reduced
to an Abel equation of the first kind. The integral curves of this equation
are constructed within the natural domain. In the self-similar solution domain,
the maximum (minimum) principal stress is constructed numerically as a function
of the polar angle in the meridional plane. |
| References |
| 1. | R. T. Shield, "On the plastic flow of metals under conditions
of axial symmetry,"
Proc. Roy. Soc. Lond., Vol. 233A, No. 1193, pp. 267-287, 1955. |
| 2. | D. D. Ivlev, "On the general equations of perfect plasticity
and statics of a granular medium,"
PMM [Applied Mathematics and Mechanics], Vol. 22, No. 1,
pp. 90-96, 1958. |
| 3. | D. D. Ivlev, Theory of Perfect Plasticity [in Russian],
Nauka, Moscow, 1966. |
| 4. | L. M. Kachanov, Fundamentals of Plasticity [in Russian],
Nauka, Moscow, 1969. |
| 5. | Yu. N. Radaev, "On Poincaré's canonical transformations
and the invariants of the plastic equilibrium equations,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 1, pp. 86-94, 1990. |
| 6. | Yu. N. Radaev, "To the theory of 3D equations of mathematical
plasticity," Izv. AN. MTT [Mechanics of Solids], No. 5, pp. 102-120, 2003. |
| 7. | Yu. N. Radaev and Yu. N. Bakhareva, "To the theory of the
axially symmetric problem of mathematical plasticity,"
Vestnik Samarsk. Gos. Un-ta. Estest. Ser.,
No. 4(30), pp. 125-139, 2003. |
|
| Received |
05 March 2003 |
| << Previous article | Volume 40, Issue 2 / 2005 | Next article >> |
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