 | | 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 40, Issue 6 / 2005 | Next article >> |
| D. A. Georgievskaya and D. V. Georgievskii, "Saint-Venant plastic flows with weakly inhomogeneous yield strength," Mech. Solids. 40 (6), 1-12 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
6 |
Pages |
1-12 |
| Title |
Saint-Venant plastic flows with weakly inhomogeneous yield strength |
| Author(s) |
D. A. Georgievskaya (Moscow)
D. V. Georgievskii (Moscow) |
| Abstract |
Among other things, the statement of the problem for an inhomogeneous
perfectly plastic medium under the Eulerian description of motion includes
finding the law of motion of Lagrangian particles along the trajectories
and the inversion of this law. If the value of a single material function,
the yield strength, in the inhomogeneous material at the initial time
slightly differs from a known (say, constant) distribution, the asymptotic
method is applied. The notions of weak inhomogeneity in the narrow and
broad sense are introduced.
The suggested method is tested for the solution of the problem on the
dilation-contraction of a weakly inhomogeneous thick-walled perfectly
plastic tube. For the main process we take the quasi-static deformation of
a tube inhomogeneous along the radius, where the inhomogeneity can be
"strong" and "discontinuous" (i.e., the solid can be a composite). For
the perturbations, we state a linearized initial-boundary value problem,
which can be solved analytically in the first approximation. The solution
reveals a relationship between the character of the given inhomogeneity and
the singularities of the solution in the first approximation with respect
to the small parameter. |
| References |
| 1. | A. A. Il'yushin, Plasticity [in Russian], Gostekhizdat, Leningrad,
1948. |
| 2. | V. V. Sokolovskii, Theory of Plasticity [in Russian], Vysshaya
Shkola, Moscow, 1969. |
| 3. | M. I. Erkhov, Theory of Perfectly Plastic Solids and Structures [in
Russian], Nauka, Moscow, 1978. |
| 4. | I. A. Kiiko, Theory of Plastic Flow [in Russian], Izd-vo MGU,
Moscow, 1978. |
| 5. | M. A. Zadoyan, 3D Plasticity Problems [in Russian], Nauka, Moscow,
1992. |
| 6. | A. Yu. Ishlinskii and D. D. Ivlev, Mathematical Theory of
Plasticity [in Russian], Fizmatlit, Moscow, 2001. |
| 7. | V. G. Zubchaninov, Mathematical Theory of Plasticity [in Russian],
Izd-vo Tversk. Un-ta, Tver, 2002. |
| 8. | B. E. Pobedrya, Mechanics of Composites [in Russian], Izd-vo MGU,
Moscow, 1984. |
| 9. | D. V. Georgievskii, D. M. Klimov, and A. G. Petrov, "On
inertia-free deformation of a weakly inhomogeneous viscous medium,"
Vestnik MGU, Ser. 1, Mat. Mekh., No. 2, pp. 37-41, 2002. |
| 10. | D. V. Georgievskii, D. M. Klimov, and A. G. Petrov, "Problems on
inertia-free flow of a weakly inhomogeneous viscous medium," Izv. RAN.
MZhG [Fluids Dynamics], No. 3, pp. 17-25, 2003. |
| 11. | A. G. Petrov, "An asymptotic method for constructing the
Poincaré map when describing transition to dynamic chaos in Hamiltonian
systems," Doklady RAN, Vol. 382, No. 1, pp. 15-19, 2002. |
| 12. | D. V. Georgievskii and D. M. Klimov, "Energy analysis of the
evolution of kinematic perturbations in weakly inhomogeneous viscous
fluids," Izv. RAN. MZhG [Fluids Dynamics], No. 2, pp. 56-67, 2000. |
| 13. | D. V. Georgievskii, "Dynamic perturbations of the undeformed
state in perfectly plastic flows," Vestnik MGU, Ser. 1, Mat. Mekh., No. 4,
pp. 45-50, 2004. |
| 14. | A. A. Il'yushin, "Deformation of a viscoplastic solid," Uchen.
Zap. MGU, Mekh., No. 39, pp. 3-81, 1940. |
|
| Received |
30 June 2005 |
| << Previous article | Volume 40, Issue 6 / 2005 | Next article >> |
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