 | | 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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| V. M. Nikireev, "The Prandtl problem for the plane stress state," Mech. Solids. 38 (1), 86-90 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
1 |
Pages |
86-90 |
| Title |
The Prandtl problem for the plane stress state |
| Author(s) |
V. M. Nikireev (Moscow) |
| Abstract |
The Prandtl solution of the problem of a punch impressed into a medium
characterized by the angle of internal friction φ and the limiting adhesion c
(the (φ,c)-material is a Coulomb material)
was obtained in the case of plane deformation [1-3].
This solution is widely used, mostly in mechanics of soils for evaluating
bearing capacity of structural bases [4]. For structures with circular horizontal
projection, the Ishlinskii-Berezantsev solution is utilized [5, 6].
No solution is known for the plane stress state [7], since such a solution
for soils would be unrealistic. However, this solution could be used
for sea ice (which has higher viscosity than river ice) in order to
evaluate the influence of ice fields on sea platforms in northern seas.
For ice sheets thicker than 30 cm, fracture occurs in the absence of
bending, i.e., without buckling [8]. |
| References |
| 1. | L. Prandtl, "On the hardness of plastic materials and cutting
resistance," in Theory of Plasticity [Russian translation], pp. 70-79, Izd-vo Inostr.
Lit-ry, Moscow, 1949. |
| 2. | A. Nadai, Theory of Flow and Fracture of Solids. Volume 2 [Russian translation],
Mir, Moscow, 1969. |
| 3. | V. V. Sokolovskii, Statics of Granular Materials [in Russian],
Nauka, Moscow, 1990. |
| 4. | V. N. Nikolaevskii, "Mechanical properties of soils and the theory
of plasticity," in Advances in Science and Technology. Mechanics of
Solids. Volume 6 [in Russian], VINITI, Moscow, 1972. |
| 5. | A. Yu. Ishlinskii,
"An axially symmetric problem of plasticity and the Brinell test,"
PMM [Applied Mathematics and Mechanics], Vol. 8, No. 3, pp. 201-224, 1944. |
| 6. | V. G. Berezantsev,
Axially Symmetric Problem of the Theory of Limiting Equilibrium of
Granular Media [in Russian], Gostekhizdat, Moscow, 1952. |
| 7. | M. V. Malyshev, Strength of Soils and Stability of Structural Bases
[in Russian], Stroiizdat, Moscow, 1980. |
| 8. | B. Michel, Ice Pressure on Engineering Structures [Russian translation],
Transport, Moscow, 1978. |
| 9. | D. C. Drucker and W. Prager,
"Soil mechanics and plastic analysis or limiting design,"
in Governing Laws in Soil Mechanics [Russian translation], pp. 166-177, Mir, Moscow,
1975. |
| 10. | V. V. Sokolovskii, Theory of Plasticity [in Russian], Vysshaya Shkola,
Moscow, 1969. |
| 11. | H. Henky, "On the slow steady-state flows in plastic bodies
with applications to rolling, pressing, and drawing,"
in Yu. N. Rabotnov (Editor), Theory of Plasticity.
Collected Papers [Russian translation], pp. 136-156, Izd-vo
Inostr. Lit-ry, Moscow, 1948. |
| 12. | R. Hill, Mathematical Theory of Plasticity [Russian translation], Gostekhizdat,
Moscow, 1956. |
| 13. | G. I. Bykovtsev and D. D. Ivlev, Theory of Plasticity [in Russian],
Dal'nauka, Vladivostok, 1998. |
|
| Received |
30 October 2000 |
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