 | | 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
|
| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 39, Issue 5 / 2004 | Next article >> |
| N. B. Kostyrin, N. V. Minaeva, and Yu. M. Myasnyankin, "Stress-strain state of nearly homogeneous elastoplastic bodies," Mech. Solids. 39 (5), 71-75 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
5 |
Pages |
71-75 |
| Title |
Stress-strain state of nearly homogeneous elastoplastic bodies |
| Author(s) |
N. B. Kostyrin (Voronezh)
N. V. Minaeva (Voronezh)
Yu. M. Myasnyankin (Voronezh) |
| Abstract |
In [1-4] an analytical method has been developed for obtaining approximate solutions of some problems describing the stress-strain state of elastoplastic bodies, with their geometric imperfections taken into account. In [5], this method is extended to inhomogeneous bodies.
In the present paper, we consider the plane-strain case and the space of parameters characterizing external disturbances on an elastoplastic body. On the basis of the implicit function theorem, we propose a method for the construction of the boundary of a region in that space in which the solution of the corresponding problem continuously depends on the characteristics describing geometric imperfections of the elastoplastic body and the inhomogeneity of its material. As an example we consider the behavior of an elastoplastic pipe subjected to internal and external pressure. |
| References |
| 1. | D. D. Ivlev, "Approximate solution of elastoplastic problems in the theory of perfect plasticity," Doklady AN SSSR, Vol. 113, No. 2,
pp. 294-296, 1967. |
| 2. | D. D. Ivlev, Mechanics of Plastic Media. Volume 2 [in Russian], Fizmatlit,
Moscow, 2002. |
| 3. | D. D. Ivlev and L. V. Ershov,
Perturbation Method in the Theory of Elastoplastic Bodies [in Russian],
Nauka, Moscow, 1978. |
| 4. | A. Yu. Ishlinskii and D. D. Ivlev,
Mathematical Plasticity [in Russian], Fizmatlit, Moscow, 2001. |
| 5. | T. L. Zakharova and D. D. Ivlev, "Approximate solution of plane problems for ideal elastoplastic inhomogeneous bodies," Zh. Prikl. Mekhaniki i Tekhn. Fiziki, Vol. 38, No. 5, pp. 165-172, 1997. |
| 6. | M. M. Filonenko-Borodich,
Theory of Elasticity [in Russian], Gostekhizdat, Moscow, 1947. |
| 7. | A. A. Il'yushin, Plasticity [in Russian], Gostekhizdat, Moscow, Leningrad, 1948. |
| 8. | A. N. Kolmogorov and S. V. Fomin, Fundamentals of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow, 1976. |
| 9. | M. A. Naimark,
Linear Differential Operators [in Russian], Nauka, Moscow, 1969. |
| 10. | N. V. Minaeva, Perturbation Method in Solid Mechanics [in Russian],
Nauchn. Kniga, Moscow, 2002. |
| 11. | N. V. Minaeva, "On the stress-strain state of thick-walled nearly-axisymmetric pipe," Izv. AN. MTT [Mechanics of Solids], No. 3,
pp. 72-77, 2002. |
| 12. | A. Yu. Ishlinskii, "Stability of equilibrium of elastic bodies from the standpoint of mathematical elasticity," Ukr. Mat. Zh., Vol. 6,
No. 2, pp. 140-146, 1954. |
|
| Received |
03 June 2003 |
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