 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| A. V. Gnoevoi, D. M. Klimov, and V. M. Chesnokov, "On one case of plane flow of Bingham media," Mech. Solids. 36 (5), 47-55 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
5 |
Pages |
47-55 |
| Title |
On one case of plane flow of Bingham media |
| Author(s) |
A. V. Gnoevoi (Moscow)
D. M. Klimov (Moscow)
V. M. Chesnokov (Moscow) |
| Abstract |
Statements of some problems for
Bingham flows with a rigid core are shown to contradict the
physical meaning of these problems. For a plane problem
of Bingham flow in a channel with deformable walls,
under the assumption that there exists a quasi-rigid
core, it is shown that the boundary conditions on the interface
between the shear and rigid regions are violated.
A thin layer approximation is considered for
the solution of the problem of plane flow of a Bingham medium between
two smooth deformable surfaces. The solution of the problem
is obtained under the assumption that there are three regions in the flow:
two regions of shear flow adjacent to the deformable surfaces
and the third region of plastic flow between these two.
The general solution obtained allows us to construct, as a special case,
the solution for the plastic flow and the solution of the Prandtl problem
for a plastic layer compressed by two rigid parallel plates.
The results are compared with those obtained by other authors. |
| References |
| 1. | A. V. Gnoevoi, D. M. Klimov, and V. M. Chesnokov,
On the Theory of Bingham Flows [in Russian], Preprint No. 626, In-t Problem
Mekhaniki RAN, Moscow, 1998. |
| 2. | M. Reiner, Deformation, Strain and Flow. An Elementary Introduction
to Rheology [Russian translation], Gostekhizdat, Moscow, 1963. |
| 3. | G. Henky, "On slow stationary flows in plastic bodies
with applications to rolling, forging and drawing," in Yu. N. Rabotnov
(Editor), Theory of Plasticity [Russian translation],
pp. 136-156, Izd-vo Inostr. Lit-ry, 1948. |
| 4. | M. P. Volarovich and A. M. Gutkin, "Viscoplastic flow between
two plane parallel walls or in
the annular space between two coaxial tubes," Zh. Tekhn. Fiziki, Vol. 16,
No. 3, pp. 321-328, 1946. |
| 5. | V. P. Myasnikov, "Flow of a viscoplastic medium with complex
shear," Zh. Prikl. Mekhaniki i Tekhn. Fiziki, No. 5, pp. 76-87, 1961. |
| 6. | P. M. Ogibalov and A. Kh. Mirzadzhanzade,
Nonstationary Motion of Viscoplastic Media [in Russian], Izd-vo MGU,
Moscow, 1977. |
| 7. | V. P. Myasnikov, "On the compression of a viscoplastic layer by
rigid plates," Izv. AN SSSR. Mekh. i Mashinostr., No. 4, pp. 92-96, 1963. |
| 8. | G. G. Lipscomb and M. M. Denn,
"Flow of Bingham fluids in complex geometries,"
Non-Newt. Fluid. Mech., Vol. 14, No. 4, pp. 337-346, 1984. |
| 9. | L. M. Kachanov, Principles of the Theory of Plasticity [in Russian],
Nauka, Moscow, 1969. |
| 10. | A. V. Gnoevoi, D. M. Klimov, and V. M. Chesnokov,
A Study of Viscoplastic Flows in Channels and Cavities with
Variable Shape of Their Walls [in Russian], Poligrafservis, Moscow, 1995. |
| 11. | B. Saint-Venant, "On the derivation of equations of interior
motions arising in solid plastic bodies beyond the limits of elasticity,"
in Yu. N. Rabotnov (Editor), Theory of Plasticity, Izd-vo Inostr. Lit-ry,
Moscow, 1948. |
| 12. | M. D. Van Dyke, Perturbation Methods in Fluid Mechanics [Russian translation],
Mir, Moscow, 1967. |
| 13. | N. N. Malinin, Applied Theory of Plasticity and Creep [in Russian],
Mashinostroenie, Moscow, 1975. |
|
| Received |
18 September 2000 |
| << Previous article | Volume 36, Issue 5 / 2001 | Next article >> |
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