| | 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: | | 12804 |
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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In English (Mech. Solids): | | 4760 |
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<< Previous article | Volume 46, Issue 4 / 2011 | Next article >> |
Z.V. Nagoev and M.M. Oshkhunov, "Discrete-Dynamic Particle Method in Problems of Mechanics of Deformable Solids," Mech. Solids. 46 (4), 622-634 (2011) |
Year |
2011 |
Volume |
46 |
Number |
4 |
Pages |
622-634 |
DOI |
10.3103/S0025654411040121 |
Title |
Discrete-Dynamic Particle Method in Problems of Mechanics of Deformable Solids |
Author(s) |
Z.V. Nagoev (Institute of Computer Science and Problems of Regional Administration, Kabardino-Balkar Scientific Center, Russian Academy of Sciences, I. Armand 37a, Nalchik, 360000 Russia, zaliman@mail.ru)
M.M. Oshkhunov (Institute of Computer Science and Problems of Regional Administration, Kabardino-Balkar Scientific Center, Russian Academy of Sciences, I. Armand 37a, Nalchik, 360000 Russia, muaed@inbox.ru) |
Abstract |
We suggest a discrete-dynamic method for solving problems of mechanics of deformable solids, analyze the relation between this model and the classical theory of elasticity, interpret physical and mechanical constants, and compare the solutions obtained by the dynamic particle method with the well-known solutions of some problems of the theory of elasticity. |
Keywords |
discrete-dynamic particle method, Hooke law, physically and geometrically nonlinear elasticity |
References |
1. | Yu. A. Amenzade,
Theory of Elasticity
(Vysshaya Shkola, Moscow, 1971)
[in Russian]. |
2. | A. E. H. Love,
A Treatise on the Mathematical Theory of Elasticity, 4th ed.
(Cambridge Univ. Press, Cambridge, 1927; ONTI, Moscow, 1935). |
3. | N. I. Muskhelishvili,
Some Fundamental Problems of Mathematical Elasticity Theory (Plane Theory)
(Nauka, Moscow, 1966)
[in Russian]. |
4. | V. V. Novozhilov,
Theory of Elasticity
(Sudpromgiz, Moscow, 1958)
[in Russian]. |
5. | Yu. N. Rabotnov,
Mechanics of Deformable Solids
(Nauka, Moscow, 1979)
[in Russian]. |
6. | D. L. Bykov,
"On Some Methods for Solving Problems of the Theory of Plasticity,"
in Elasticity and Nonelasticity, No. 4
(Izd-vo MGU, Moscow, 1975),
pp. 119-139
[in Russian]. |
7. | D. L. Bykov,
"On Some Relations between Stress and Strain Invariants in Physically Nonlinear Media,"
in Elasticity and Nonelasticity, No. 2
(Izd-vo MGU, Moscow, 1971),
pp. 114-128
[in Russian]. |
8. | A. A. Il'yushin,
Plasticity. Foundations of Mathematical Theory
(Izd-vo AN SSSR, Moscow, 1963)
[in Russian]. |
9. | M. M. Oshkhunov,
"Rate of Convergence of Iterative Processes in Nonlinear Elasticity,"
Prikl. Mekh.
31 (1), 86-90 (1995)
[Int. Appl. Mech. (Engl. Transl.)
31 (1), 79-82 (1995)]. |
10. | M. M. Oshkhunov and G. I. Komarov,
"On the Solvability of Physically Nonlinear Problems of Thermoelasticity,"
Ukrain. Mat. Zh.
48 (7), 949-953 (1996)
[Ukrain. Math. J. (Engl. Transl.)
48 (7), 1074-1078 (1996).]. |
11. | M. M. Oshkhunov and S. Ozden,
"The General Stress and Strain Relationship in Nonlinear Materials,"
Int. J. Nonlin. Mech.
35, 763-767 (2000). |
12. | O. C. Zienkiewicz,
The Finite Element Method in Engineering Science
(McGraw-Hill, New York, 1971; Mir, Moscow, 1975). |
13. | H. Kardestuncer,
Finite Element Hand Book
(McGraw-Hill, New York, 1987). |
14. | R. W. Hockney and J. W. Eastwood,
Computer Simulation Using Particles
(McGraw-Hill, New York, 1981; Mir, Moscow, 1987). |
15. | M. M. Oshkhunov, T. M. Batashov, R. D. Eleeva, and I. A. Mamieva,
"Numerical Solution of Equations by the Dynamical Particle Method,"
in Science and Technology in the XXIst Century,
Proc. 3rd Intern. Sci.-Techn. Conf., Vol. 2
(KBGU, Nalchik, 2007), pp. 41-46
[in Russian]. |
16. | A. A. Samarskii,
Introduction to the Theory of Difference Schemes
(Nauka, Moscow, 1971)
[in Russian]. |
17. | R. W. Hamming,
Numerical Methods. For Scientists and Engineers
(McGraw-Hill, New York, 1962; Nauka, Moscow, 1972). |
18. | M. M. Oshkhunov and R. B. Tkhakakhov,
"Mathematical Models and Methods for Computations of Polyvinylchloride Compositions,"
Plastich. Massy,
No. 11, 43-47 (2007). |
19. | M. M. Oshkhunov and S. Ozden,
"The Conditions of Minimum Potential Energy and Castigliano's Functional in Nonlinear Media,"
Int. J. Nonlin. Mech.
38 (2), 71-77 (2003). |
20. | A. M. Krivtsov and N. V. Krivtsova,
"Method of Particles and Its Application to Mechanics of Solids,"
Dalnevost. Matem. Zh. DVO RAN
3 (2), 254-276 (2002). |
21. | S. P. Timoshenko and J. N. Goodyear,
Theory of Elasticity
(McGraw-Hill, New York, 1951; Nauka, Moscow, 1975). |
|
Received |
29 May 2008 |
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