 | | 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
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| In English (Mech. Solids): | | 3212 |
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| A. S. Kravchuk, "Development of a solution method for frictional contact problems with complex loading," Mech. Solids. 42 (3), 346-355 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
3 |
Pages |
346-355 |
| Title |
Development of a solution method for frictional contact problems with complex loading |
| Author(s) |
A. S. Kravchuk (Moscow State University of Instrument Engineering and Computer Science, Stromynka 20, Moscow, 107996, Russia, kravchuk_biocom@mail.ru) |
| Abstract |
In this work, solution methods for frictional contact problems are extended to the case of moving punches and to the external loading history-dependent system states. To solve the frictional contact problems in the contact area, an iterative method is developed and implemented. Solutions of two-dimensional problems are constructed using the boundary element method. Numerical analysis is aimed at the quantitative study of effects such as the interaction of contact pressure and friction forces, estimates of the friction force differences due to the differences in the choice of local basis for the calculation of normal pressure and friction forces, and evaluation of the effects of complex loading (rotation of the rigid punch after its preliminary penetration into the solid). We find that, for the same definition of the friction force, different initial approximations lead to the same solution. At the same time, the friction forces defined either as projections onto the common tangent plane or as projections onto the plane tangent to the punch can differ quite substantially. Similar conclusions are derived for the solutions corresponding to single or multiple loading steps. The work relies on the variational principle for the solution of contact problems and numerical algorithms developed for the problems with one-sided constraints. The variational principle was first applied by Signorini [1] to the determination of the stress-strain state in a linearly deformed body in a rigid smooth shell. The modern view of the problem and its generalizations to the frictional problems and some other problems involving unilateral constraints in given in the monograph [2]. Finite difference and finite element methods in application to the problems with unilateral constraints are described in [3]. Analytical solution methods are developed in the monographs [4–6]. |
| References |
| 1. | A. Signorini,
"Sopra alcune questioni di elastostatica,"
Atti Soc. Ital. Progr. Sei.,
513-533 (1933). |
| 2. | G. Duvaut and J.-L. Lions, Les Inéquations en Méchanique
et en Physique (Dunod, Paris, 1972). |
| 3. | R. Glowinski, J. L. Lions, and R. Trémolieres, Numerical
Analysis for Variational Inequalities (North Holland, Amsterdam,
1981). |
| 4. | I. G. Goryacheva,
Mechanics of Friction Interaction
(Nauka, Moscow, 2001) [in Russian]. |
| 5. | G. M. L. Gladwell,
Contact Problems in the Classical Theory of Elasticity
(Sijthoff and Noordhoff, Alphen aan den Rijn, 1980). |
| 6. | V. M. Alexandrov and D. A. Pozharskii, Nonclassical Spatial
Problems of Mechanics of Contact Interaction of Elastic Bodies
(Factorial, Moscow, 1998) [in Russian]. |
| 7. | S. S. Grigoryan, "A New Law of Friction and Mechanism for
Large-Scale Rock Avalanches and Landslides," Dokl. Akad. Nauk
SSSR 244 (4), 846-849 (1979) [Soviet Math. Dokl.]. |
| 8. | A. S. Kravchuk,
"To the Theory of Frictional Contact Problems,"
Prikl. Mat. Mekh.
44 (1), 122-129 (1980)
[J. Appl. Math. Mech. (Engl. Transl.)]. |
| 9. | A. S. Kravchuk, Variational and Quasivariational Inequalities
in Mechanics (Izd-vo MGAPI, Moscow, 1997) [in Russian]. |
| 10. | A. S. Kravchuk and P. Neittaanmyaki, "Variational Method for the
Solution of Dynamic Frictional Contact Problems," in Proc.
3rd All-Russian Conf. on Elasticity, Rostov-on-Don, 2004 (Novaya
Kniga, Rostov-on-Don, 2004), pp. 238-240. |
| 11. | C. A. Brebbia, J. C. F. Telles, and L. C. Wrobel, Boundary
Element Techniques. Theory and Applications in Engineering
(Springer, Berlin, 1984; Mir, Moscow, 1987). |
| 12. | J.-L. Lions, "Surface Problems: Methods of Variational and
Quasivariational Inequalities," in Lect. Notes in Math. Syst.
(461) (Springer, Berlin, 1975), pp. 129-148. |
| 13. | N. I. Muskhelishvili,
Some Fundamental Problems of Mathematical Elasticity Theory
(Nauka, Moscow, 1966)
[in Russian]. |
|
| Received |
07 July 2005 |
| Link to Fulltext |
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