 | | 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.A. Zelenina and L.M. Zubov, "One-Dimensional Deformations of Nonlinearly Elastic Micropolar Bodies," Mech. Solids. 45 (4), 575-582 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
4 |
Pages |
575-582 |
| DOI |
10.3103/S0025654410040072 |
| Title |
One-Dimensional Deformations of Nonlinearly Elastic Micropolar Bodies |
| Author(s) |
A.A. Zelenina (South Federal University, Mil'chikova 8a, Rostov-on-Don, 344090 Russia, zelenina@math.rsu.ru)
L.M. Zubov (South Federal University, Mil'chikova 8a, Rostov-on-Don, 344090 Russia, zubov@math.rsu.ru) |
| Abstract |
We find families of finite deformations of a Cosserat elastic continuum on which the system of equilibrium equations is reduced to a system of ordinary differential equations. These families can be used to describe the expansion, tension, and torsion of a hollow circular cylinder, cylindrical bending of a rectangular slab, straightening of a circular arch, reversing of a cylindrical tube, formation of screw and wedge dislocations in a hollow cylinder, and other types of deformations. In the case of a physically nonlinear material model, the above-listed families of deformations can be used to construct exact solutions of several problems of strong bending of micropolar bodies. |
| References |
| 1. | R. A. Toupin,
"Theories of Elasticity with Couple-Stress,"
Arch. Ration. Mech. and Anal.
17 (2), 85-112 (1964). |
| 2. | L. I. Shkutin,
Mechanics of Deformations of Flexible Bodies
(Nauka, Novosibirsk, 1997)
[in Russian]. |
| 3. | L. M. Zubov,
Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies
(Springer, Berlin, 1997). |
| 4. | E. Nikitin and L. M. Zubov,
"Conservation Laws and Conjugate Solutions in the Elasticity of Simple Materials
and Materials with Couple Stress,"
J. Elasticity
51 (1), 1-22 (1998). |
| 5. | L. M. Zubov and M. I. Karyakin,
Tensor Calculus. Foundations of the Theory
(Vuzovskaya Kniga, Moscow, 2006)
[in Russian]. |
| 6. | A. E. Green and J. E. Adkins,
Large Elastic Deformations and Non-Linear Continuum Mechanics
(Clarendon Press, Osford, 1960; Mir, Moscow, 1965). |
| 7. | L. M. Zubov,
"A Semi-Inverse Method in Quasistatic Problems of Nonlinear Thermoviscoelasticity,"
Dokl. Akad. Nauk SSSR
256 (3), 556-559 (1981)
[Soviet Phys. Dokl. (Engl. Transl.)
26, 111 (1981)]. |
| 8. | A. I. Lurie,
Nonlinear Theory of Elasticity
(Nauka, Moscow, 1980)
[in Russian]. |
| 9. | A. A. Zelenina,
"Theory of Large-Strain Torsion of Prismatic Bodies with Moment Stresses,"
Zh. Prikl. Mekh. Tekh. Fiz.
47 (4), 167-175 (2006)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
47 (4), 600-607 (2006)]. |
|
| Received |
13 January 2010 |
| Link to Fulltext |
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