 | | 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
|
| In English (Mech. Solids): | | 3212 |
|
| << Previous article | Volume 43, Issue 2 / 2008 | Next article >> |
| V. V. Korepanov, V. P. Matveenko, and I. N. Shardakov, "Numerical study of two-dimensional problems of nonsymmetric elasticity," Mech. Solids. 43 (2), 218-224 (2008) |
| Year |
2008 |
Volume |
43 |
Number |
2 |
Pages |
218-224 |
| DOI |
10.3103/S0025654408020064 |
| Title |
Numerical study of two-dimensional problems of nonsymmetric elasticity |
| Author(s) |
V. V. Korepanov (Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Ul. Akad. Koroleva 1, Perm, 614013, Russia, kvv@icmm.ru)
V. P. Matveenko (Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Ul. Akad. Koroleva 1, Perm, 614013, Russia, mvp@icmm.ru)
I. N. Shardakov (Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Ul. Akad. Koroleva 1, Perm, 614013, Russia, shardakov@icmm.ru) |
| Abstract |
We consider the algorithm of the finite element method for solving two-dimensional problems of nonsymmetric elasticity. We discuss the possibilities of the algorithm and its efficiency by comparing the numerical results with the well-known analytic solutions. We present the results obtained by solving the problem of tension of a plate weakened by a series of holes and the problem of tension for a plate with a central crack. The numerical results thus obtained are considered as an addition to the analytic solutions in the context of experimental justification of couple-stress effects arising under deformation of elastic materials and in the context of solving the identification problem for mechanical constants in nonsymmetric elasticity. |
| References |
| 1. | W. Nowacki,
Theory of Elasticity
(PWN, Warsaw, 1970; Mir, Moscow, 1975). |
| 2. | V. A. Pal'mov,
"Fundamental Equations of the Theory of Asymmetric Elasticity,"
"Fundamental Equations of the Theory of Nonsymmetric Elasticity,"
Prikl. Mat. Mekh.
28 (3), 401-408 (1964)
[J. Appl. Math. Mech. (Engl. Transl.)
28 (3), 496-505 (1964)]. |
| 3. | A. C. Eringen,
Micropolar Field Theories, Vol. II: Failure, Ed. by G. Liboviz
(Mir, Moscow, 1975),
pp. 647-751
[in Russian]. |
| 4. | R. D. Gauthier and W. E. Jahsman,
"A Quest for Micropolar Elastic Constants,"
Trans. ASME Ser. E. J. Appl. Mech.
42 (2), 369-374 (1975). |
| 5. | R. S. Lakes,
"Experimental Methods for Study of Cosserat Elastic Solids
and Other Generalized Continua,"
in Continuum Models for Materials with Micro-Structure,
Ed. by H. Muhlhaus
(Wiley, New York, 1995),
pp. 1-22. |
| 6. | R. D. Mindlin,
"Influence of Couple-Stress on Stress Concentrations,
Experim. Mech.
3 (1), 1-7 (1963). |
| 7. | V. A. Pal'mov,
"The Plane Problem in the Theory of Nonsymmetrical Elasticity,"
Prikl. Mat. Mekh.
28 (6), 1117-1120 (1964)
[J. Appl. Math. Mech. (Engl. Transl.)
28 (6), 1341-1345 (1964)]. |
| 8. | M. Onami, S. Ivasimidzu, K. Genka, et al.,
Introduction to Micromechanics
(Metallurgiya, Moscow, 1987)
[in Russian]. |
| 9. | W. T. Koiter,
"Couple-Stress in the Theory of Elasticity,"
Proc. Könicl. Acad. Wet.
B67 (17), 89-112 (1964). |
| 10. | E. Kröner,
"On the Physical Reality of Torque Stresses in Continuum Mechanics,"
Intern. J. Eng. Sci.
1 (2), 261-278 (1963). |
| 11. | M. A. Kulesh, V. P. Matveenko, and I. N. Shardakov,
"Construction of Analytical Solutions of Some Two-Dimensional
Problems in the Moment Theory of Elasticity,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 69-82 (2002)
[Mech. Solids (Engl. Transl.)
37 (5), 56-67 (2002)]. |
| 12. | M. A. Kulesh, V. P. Matveenko, and I. N. Shardakov,
"Parametric Analysis of Analytical Solution to
One- and Two-Dimensional Problems in Couple-Stress Theory of Elasticity,"
ZAMM
83 (4), 238-248 (2003). |
| 13. | S. Nakamura, R. L. Benedict, and R. S. Lakes,
"Finite Element Method for Orthotropic Micropolar
Elasticity,"
Intern. J. Eng. Sci
22 (3), 319-330 (1984). |
| 14. | S. Nakamura and R. S. Lakes,
"Finite Element Analysis of Stress Concentration around a Blunt Crack
in a Cosserat Elastic Solid,"
Comput. Methods in Appl. Mech. and Eng.
66 (3), 257-266 (1988). |
| 15. | O. C. Zienkiewicz,
Finite Element Method in Engineering Science
(McGraw-Hill Education, London, 1971; Mir, Moscow, 1975). |
|
| Received |
28 August 2005 |
| Link to Fulltext |
|
| << Previous article | Volume 43, Issue 2 / 2008 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English