 | | 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
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| In English (Mech. Solids): | | 4760 |
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| D. V. Georgievskii, "The Prandtl problem for a plastic layer weakly inhomogeneous with respect to the yield strength," Mech. Solids. 41 (1), 35-45 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
1 |
Pages |
35-45 |
| Title |
The Prandtl problem for a plastic layer weakly inhomogeneous with respect to the yield strength |
| Author(s) |
D. V. Georgievskii (Moscow) |
| Abstract |
The analysis of the sensitivity of the deformation parameters to perturbations
of material functions plays an important role (in both academic and applied
aspects) in continuum mechanics, especially in problems with mixed boundary
conditions [1]. The statement of the problem for an inhomogeneous continuous
medium in the case of Eulerian description of the motion involves, in
particular, the determination of the law of motion of Lagrangian particles
along their trajectories and the inversion of this law. If at the initial time
instant the difference of the material functions in an inhomogeneous material
from some familiar distributions (e.g., constant distributions) is small, one
can use the asymptotic method of [2]. This method is tested on the problem of
compression of a thin perfectly plastic layer weakly inhomogeneous with respect
to the yield strength by rigid plates. As the basic process we choose the
quasistatic deformation of a homogeneous medium. This process corresponds to
Prandtl's solution. A linear initial-boundary value problem is formulated for
the perturbations. For some particular cases of the initial inhomogeneity this
problem can be solved analytically. |
| References |
| 1. | V. M. Alexandrov and E. V. Kovalenko, Problems of Cotinuum Mechanics
with Mixed Boundary Conditions [in Russian], Nauka, Moscow, 1986. |
| 2. | D. V. Georgievskii, "Modeling of weak inhomogeneity in the case of the
Eulerian description of a continuous medium," Doklady RAN, Vol. 405, No. 4,
pp. 497-483, 2005. |
| 3. | A. A. Il'yushin, Plasticity. Part 1. Elastoplastic Deformations [in
Russian], Logos, Moscow, 2004. |
| 4. | V. V. Sokolovskii, Theory of Plasticity [in Russian], Vysshaya Shkola,
Moscow, 1969. |
| 5. | M. I. Erkhov, Theory of Perfectly Plastic Bodies and Structures [in
Russian], Nauka, Moscow, 1978. |
| 6. | M. A. Zadoyan, Spatial Problems of Plasticity [in Russian], Nauka,
Moscow, 1992. |
| 7. | A. Yu. Ishlinskii and D. D. Ivlev, Mathematical Theory of Plasticity
[in Russian], Fizmatlit, Moscow, 2001. |
| 8. | V. G. Zubchaninov, Mathematical Theory of Plasticity [in Russian],
Izd-vo TvGTU, Tver, 2002. |
| 9. | D. A. Georgievskaya and D. V. Georgievskii, "Saint-Venant plastic
flows weakly inhomogeneous with respect to the yield strength," Izv. RAN. MTT
[Mechanics of Solids], No. 6, pp. 11-25, 2005. |
| 10. | A. A. Il'yushin, "Deformation of a viscoplastic body," Uchenye
Zapiski MGU. Mekhanika, Issue 39, pp. 3-81, 1940. |
| 11. | A. G. Petrov, "An asymptotic method for constructing the Poincaré
mapping to describe the transition to the dynamic chaos in Hamiltonian
systems," Doklady RAN, Vol. 382, No. 1, pp. 15-19, 2002. |
| 12. | I. A. Kiiko, "A generalization of L. Prandtl's problem of the
settlement of a strip from a compressible material," Vestnik MGU [Bulletin of
the Moscow State University], Ser. 1. Matematika. Mekhanika, No. 4, pp. 47-52,
2002. |
| 13. | I. A. Kiiko and V. A. Kadymov, "A generalization of L. Prandtl's
problem of the compression of a strip," Vestnik MGU [Bulletin of the Moscow
State University], Ser. 1. Matematika. Mekhanika, No. 4, pp. 50-56, 2003. |
| 14. | V. L. Kolmogorov, Mechanics of Metal Plastic Working [in Russian],
Izd-vo UrGTU-UPI, Ekaterinburg, 2001. |
| 15. | B. E. Pobedrya, Mechanics of Composite Materials [in Russian], Izd-vo
MGU, Moscow, 1984. |
| 16. | B. E. Pobedrya and I. L. Guzei, "Mathematical modeling of deformation
of composites with the thermal diffusion being taken into account,"
Matematicheskoe Modelirovanie Sistem i Protsessov, No. 6, pp. 82-91, 1998. |
| 17. | V. Kadymov and R. Wille, "Plastic flow in piecewise-homogeneous
layers," ZAMM, B. 75, No. 1, S. 293-294, 1995. |
|
| Received |
05 June 2005 |
| << Previous article | Volume 41, Issue 1 / 2006 | Next article >> |
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