 | | 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 |
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| S. V. Sheshenin, "Three-dimensional modeling of tires," Mech. Solids. 42 (3), 338-345 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
3 |
Pages |
338-345 |
| Title |
Three-dimensional modeling of tires |
| Author(s) |
S. V. Sheshenin (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992, Russia, shesheni@mech.math.msu.su) |
| Abstract |
Modeling the stress-strain state of pneumatic tires in the conditions of steady-state and transient rolling is of interest for mechanics of composites and computational mechanics and important from the applied point of view. Mechanical models of various levels of complexity can be used for numerical modeling. In quite a few papers, the corresponding models are derived from the theory of orthotropic shells [1]. However, more thorough and accurate studies of the stress-strain state can be carried out on the basis of three-dimensional models based on the elasticity or viscoelasticity equations. As far as Russian authors are concerned, this approach has first been suggested and implemented in [2]. Another, combined approach uses both the shell theory and the three-dimensional equations of elasticity theory [3, 4]. This approach is reasonable, because the tire structure includes both volumes filled with rubber and thin layers of the rubber cord. The rubber cord layers can be considered as a composite whose structural components possess very different properties. Also, it is quite admissible to consider the rubber cord as a structure periodic in the horizontal projection. Note that the mathematical theory of periodic composites has been developed in [5]. Owing to strong anisotropy and inhomogeneity of the material, large shape distortions of the tire, and, in some cases, its large deformations, viscoelastic properties of rubber play an important role, so that the mechanic model of the tire turns out to be quite complex. The large property differences between various structural components make the matrix of the resulting system of linear equations ill-conditioned, which complicates its numerical solution [6].
In this paper, theoretical aspects of a three-dimensional tire model and its numerical implementation are considered. |
| References |
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(Khimiya, Moscow, 1988) [in Russian]. |
| 2. | B. E. Pobedrya and S. V. Sheshenin,
"3D Modeling of Pneumatic Tires. Part 1,"
in 8th Symp. "Problemi Shin i Rezinokordhykh Kompozitov," Moscow, 1997
(Moscow, 1997),
Vol. 2, pp. 320-326. |
| 3. | G. M. Kulikov and S. V. Plotnikiva,
"Geometrically Exact Assumed
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Comput. and Struct.
84 (19-20), 1275-1287 (2006). |
| 4. | S. V. Sheshenin and P. N. Demidovich, "Application of the
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A. A. Ilyushin's 95th Annivesary, Moscow, Russia, 2006 (URSS,
Moscow, 2006), pp. 433-437. |
| 5. | B. E. Pobedrya,
Mechanics of Composite Materials
(Izd-vo MGU, Moscow, 1984)
[in Russian]. |
| 6. | B. E. Pobedrya,
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Elasticity and Plasticity
(Izd-vo MGU, Moscow, 1981)
[in Russian]. |
| 7. | N. M. Newmark,
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8 (3), 67-94 (1959). |
| 8. | A. I. Lurie,
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| 10. | L. Nasdala, M. Kaliske, A. Becker, and H. Rothert,
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Comput. Mech.
22 (5), 395-403 (1998). |
| 11. | H. Rothert, H. Idelberger, and W. Jacobi,
"On the Finite Element Solution of the Threedimensional Tire Contact Problem,"
Nucl. Eng. Des.
78 (3), 363-375 (1984). |
| 12. | K. F. Chernykh,
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[in Russian]. |
| 13. | Y. Nakayama and J. Padovan,
"Finite Element Analysis of Steady and Transiently Moving/Rolling
Nonlinear Viscoelastic Structure - Impact/Contact Simulations,"
Comput. and Structures
27 (2), 275-286 (1987). |
| 14. | S. V. Sheshenin, I. S. Kuz', and I. A. Savel'eva,
"On the Method of Stepwise Linearization in Nonlinear Elasticity Problems,"
in Elasticity and Inelasticity, Part 1 (Izd-vo MGU, Moscow, 1993),
pp. 88-94
[in Russian]. |
| 15. | J. C. Simo and T. A. Laursen,
"An Augmented Lagrangian Treatment of Contact Problems Involving Friction,"
Comput. and Structures
42 (1), 97-116 (1992). |
| 16. | B. E. Pobedrya and S. V. Sheshenin,
"On Methods of Elastic Solutions,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 5, 59-72 (1987)
[Mech. Solids (Engl. Transl.)]. |
| 17. | B. E. Pobedrya, S. V. Sheshenin, and T. Kholmatov,
Problem in Terms of Stresses
(FAN, Tashkent, 1988)
[in Russian]. |
| 18. | B. E. Pobedrya and V. A. Mol'kov,
"Effective Elastic Moduli of Fiber and Multilayered Fiber Composites,"
Vychisl. Mekh. Deformiruemogo Tverdogo Tela
1, 41-63 (1990). |
| 19. | T. Akasaka,
"Structural Mechanics of Radial Tires,"
Rubber Chemistry and Technology
54 (1), 3-29 (1979). |
| 20. | S. V. Sheshenin, "Application of Averaging Method to Plates
Periodic in the Horizontal Projection,"
Vestnik Moskov. Univ. Ser. I. Mat. Mekh.,
No. 1, 47-51 (2006)
[Moscow Univ. Math. Bull.]. |
| 21. | S. V. Sheshenin,
"Asymptotic Analysis of Plates with Periodic Cross-Sections,"
Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 71-79
(2006) [Mech. Solids (Engl. Transl.)]. |
|
| Received |
15 February 2007 |
| Link to Fulltext |
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