 | | 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
|
| In English (Mech. Solids): | | 4810 |
|
| << Previous article | Volume 47, Issue 1 / 2012 | Next article >> |
| S.O. Sargsyan, "General Theory of Thin Plates on the Basis of Nonsymmetric Theory of Elasticity," Mech. Solids. 47 (1), 119-136 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
1 |
Pages |
119-136 |
| DOI |
10.3103/S0025654412010128 |
| Title |
General Theory of Thin Plates on the Basis of Nonsymmetric Theory of Elasticity |
| Author(s) |
S.O. Sargsyan (Nalbandian Gyumri State Pedagogical Institute, Paruyr Sevaki 4, Gyumri, 377501 Armenia, armenuhis@mail.ru, afarmanyan@yahoo.com) |
| Abstract |
The paper uses the asymptotically justified hypothesis method to construct three different general refined theories of micropolar thin elastic plates, depending on the values of physical dimensionless material parameters,
involving:
(i) independent displacement and rotation fields, (ii) constrained rotation, and (iii) low shear stiffness.
All angular shear deformations are taken into account. |
| Keywords |
nonsymmetric elasticity, plates, shells, theory, free rotation, constrained rotation |
| References |
| 1. | V. E. Panin (Editor),
Physical Mesomechanics and Computer Simulation of Materials, Vol. 1
(Nauka, Novosibirsk, 1995)
[in Russian]. |
| 2. | N. F. Morozov,
"Structure Mechanics of Materials and Structural Elements.
Interaction between Nano-Micro-Meso- and Macro-Scales
in Deformation and Fracture,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 188-189 (2005). |
| 3. | R. V. Goldstein and N. F. Morozov,
"Mechanics of Deformation and Fracture of Nanomaterials and Nanotechnology,"
Fiz. Mezomekh.
10 (5), 17-30 (2007)
[Phys. Mesomech. (Engl. Transl.)
10 (5-6), 235-246 (2007)]. |
| 4. | E. A. Ivanova, A. M. Krivtsov, and N. F. Morozov,
"Derivation of Macroscopic Relations of the Elasticity of Complex Crystal
Lattices Taking into Account the Moment Interactions at the Microlevel,"
Prikl. Mat. Mekh.
71 (4), 595-615 (2007)
[J. Appl. Math. Mech. (Engl. Transl.)
71 (4), 543-561 (2007)]. |
| 5. | A. S. J. Suiker, A. V. Metrikine, and R. De Borst,
"Comparison of Wave Propagation Characteristics
of the Cosserat Continuum Model and Corresponding Discrete Lattice Models,"
Int. J. Solids Struct.
38 (9), 1563-1583 (2001). |
| 6. | V. I. Erofeev,
Wave Processes in Solids with Microstructure
(Izd-vo MGU, Moscow, 1999)
[in Russian]. |
| 7. | I. S. Pavlov and A. I. Potapov,
"Two-Dimensional Model of a Granular Medium,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 98-109 (2007)
[Mech. Solids (Engl. Transl.)
42 (2), 250-259 (2007)]. |
| 8. | S. A. Lisina and A. I. Potapov,
"Generalized Continuum Models in Nanomechanics,"
Dokl. Ross. Akad. Nauk
420 (3), 328-330 (2008)
[Dokl. Phys. (Engl. Transl.)
53 (5), 275-277 (2008)]. |
| 9. | V. V. Korepanov, M. A. Kulish, V. P. Matveenko, and I. N. Shardakov,
"Analytical and Numerical Solutions for Static and Dynamic Problems
of the Asymmetric Theory of Elasticity,"
Fiz. Mezomekh.
10 (5), 77-90 (2007)
[Phys. Mesomech. (Engl. Transl.)
10 (5-6), 281-293 (2007)]. |
| 10. | I. Yu. Smolin,
"Using Micropolar Models to Describe Plastic Deformation at Mesolevel,"
in Mathematical Modeling of Systems and Processes, No. 14
(Izdat. PGTU, Perm, 2006),
pp. 189-205
[in Russian]. |
| 11. | A. I. Lur'e and P. A. Belov,
"Variational Statement of Mathematical Models of Media with Microstructures,"
in Mathematical Modeling of Systems and Processes, No. 14
(Izd-vo PGTU, Perm, 2006), pp. 114-132
[in Russian]. |
| 12. | A. C. Eringen,
Microcontinuum Field Theories.
Vol. 1: Foundation and Solids
(Springer, New York, 1999). |
| 13. | M. Onami (Editor),
Introduction to Micromechanics,
(Metallurgiya, Moscow, 1987)
[in Russian]. |
| 14. | R. D. Gauthier and W. E. Jahsman,
"A Quest for Micropolar Elastic Constants. Part II,"
Arch. Mech.
33 (5), 717-737 (1981). |
| 15. | R. Lakes,
"Experimental Methods for Study of Cosserat Elastic Solids
and Other Generalized Elastic Continua,"
in Continuum Models for Materials with Micro-Structure,
Ed. by H. Muhlhaus
(Wiley, New York, 1995),
No. 1,
pp. 1-22. |
| 16. | A. E. Green and P. M. Naghdi,
"The Linear Elastic Cosserat Surface and Shell Theory,"
Int. J. Solids Struct.
4 (6), 585-592 (1968). |
| 17. | V. A. Palmov and H. Altenbach,
"Über eine Cosseratsche Theorie für Elastische Platen,"
Thechn. Mech.
3 (3), 3-9 (1982). |
| 18. | V. A. Palmov,
"Simplest Noncontradictory System of Equations
of the Theory of Thin Elastic Shells,"
in Mechanics of Solids
(Nauka, Moscow, 1986),
pp. 106-112
[in Russian]. |
| 19. | P. A. Zhilin,
"Basic Equations of Nonclassical Theory of Shells,"
in Dynamics and Strength of Machines. Proc. Leningrad Polytech. Inst.,
No. 386 (1982),
pp. 29-46
[in Russian]. |
| 20. | L. I. Shkutin,
Mechanics of Deformation of Flexible Bodies
(Nauka, Novosibirsk, 1988)
[in Russian]. |
| 21. | V. A. Eremeev and L. M. Zubov,
Mechanics of Elastic Shells
(Nauka, Moscow, 2008)
[in Russian]. |
| 22. | G. A. Vanin,
"Couple-Stress Mechanics of Thin Shells,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 116-128 (2004)
[Mech. Solids (Engl. Transl.)
39 (4), 92-101 (2004)]. |
| 23. | M. Birsan,
"The Solution of Saint-Venant's Problem in the Theory of Cosserat Shells,"
J. Elasticity
74, 185-214 (2004). |
| 24. | S. A. Ambartsumyan,
Micropolar Theory of Shells and Plates
(Izd-vo NAN Armeii, Erevan, 1999)
[in Russian]. |
| 25. | S. O. Sargsyan,
"Applied One-Dimensional Theories of Beams Based on Nonsymmetric Theory of Elasticity,"
Fiz. Mezomekh.
11 (5), 41-54 (2009). |
| 26. | S. O. Sargsyan,
"Boundary-Value Problems of the Asymmetric Theory of Elasticity for Thin Plates,"
Prikl. Mat. Mekh.
72 (1), 129-147 (2008)
[J. Appl. Math. Mech. (Engl. Transl.)
72 (1), 77-86 (2008)]. |
| 27. | S. O. Sargsyan,
"The General Theory of Micropolar Thin Elastic Shells,"
Dokl. NAN RA
108 (4), 309-319 (2008). |
| 28. | S. H. Sargsyan,
"Analytic Mechanics of Bars, Plates, and Shells on Asymmetrical Theory of Elasticity,"
in Abstracts Book. 22nd Int. Cong. Theor. and Appl. Mech. ICTAM 2008.
Adelaide, Australia, 2008 (2008),
p. 228. |
| 29. | B. L. Pelekh,
Stress Concentration near Holes in Bending of Transversely Isotropic Plates
(Naukova Dumka, Kiev, 1977)
[in Russian]. |
| 30. | Ch. Decolon,
Analysis of Composite Structures
(Taylor and Frances Books, New York, 2002). |
| 31. | S. A. Ambartsumyan,
Theory of Anisotropic Plates
(Nauka, Moscow, 1987)
[in Russian]. |
| 32. | V. A. Pal'mov,
"Basic 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)]. |
| 33. | E. V. Kuvshinskii and E. L. Aero,
"Continuum Theory of Asymmetric Elasticity,"
Fiz. Tverd. Tela
5 (9), 2591-2598 (1969)
[Sov. Phys. Solid State (Engl. Transl.)]. |
| 34. | W. Nowacki,
Theory of Elasticity
(PWN, Warsaw, 1970; Mir, Moscow, 1975). |
|
| Received |
12 May 2009 |
| Link to Fulltext |
|
| << Previous article | Volume 47, Issue 1 / 2012 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English