Doubly Periodic Contact Problems for a Layer with an Unknown Contact Zone

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

Doubly periodic contact problems are considered for a layer with an unknown contact domain. One face of the layer is subjected to sliding support or rigidly fixed. The problems are reduced to integral equations the kernels of which do not contain integrals. For full contact of the other layer face with a two-dimensional sinusoidal rigid surface, the problems have exact solutions used to verify computer programs realizing the numerical method of Galanov nonlinear integral equations which allows us to determine the contact domain and the contact pressure simultaneously. Mechanical characteristics are calculated for indentation of the system of elliptic paraboloids, the passage from discrete to continuous contact zones is investigated.

About the authors

N. B. Zolotov

Don State Technical University

Email: pozharda@rambler.ru
Russia, Rostov-on-Don

D. A. Pozharskii

Don State Technical University

Author for correspondence.
Email: pozharda@rambler.ru
Russia, Rostov-on-Don

References

  1. Westergaard H.M. Bearing pressure and cracks // ASME J. Appl. Mech. E., 1939, vol. 6, no. 1, pp. 43–53.
  2. Pozharskii D.A. Periodic contact and mixed problems of the elasticity theory (review) // Izv. vuzov. Severo-Kavkazskii Region. Estestvennye Nauki, 2021, no. 2, pp. 22–33. (in Russian)
  3. Goryacheva I.G. The periodic contact problem for an elastic half-space // JAMM, 1998, vol. 62, no. 6, pp. 959–966.
  4. Goryacheva I.G. Contact Mechanics in Tribology. Berlin: Springer, 1998. 360 p.
  5. Johnson K.L., Greenwood J.A., Higginson J.G. The contact of elastic regular wavy surfaces // Int. J. Mech. Sci., 1985, vol. 27, no. 6, pp. 383–396.
  6. Johnson K.L. Contact Mechanics. Cambridge: Univ. Press, 1985. 468 p.
  7. Yastrebov V.A., Anciaux G., Molinari J.-F. The contact of elastic regular wavy surfaces revisited // Tribol. Lett., 2014, vol. 56, pp. 171–183.
  8. Aleksandrov V.M. Doubly periodic contact problems for and elastic layer // JAMM, 2002, vol. 66, no. 2, pp. 297–305.
  9. Soldatenkov I.A. The periodic contact problem of the plane theory of elasticity. Taking friction, wear and adhesion into account // JAMM, 2013, vol. 77, no. 2, pp. 245–255.
  10. Goryacheva I.G., Torskaya E.V. Modeling of fatigue wear of a two-layered elastic half-space in contact with periodic system of indenters // Wear, 2010, vol. 268, no. 11–12, pp. 1417–1422.
  11. Jin F., Wan Q., Guo X. A double-Westergaard model for adhesive contact of a wavy surface // Int. J. Solids Struct., 2016, vol. 102–103, pp. 66–76.
  12. Goryacheva I.G., Makhovskaya Y. Combined effect of surface microgeometry and adhesion in normal and sliding contacts of elastic bodies // Friction, 2017, vol. 5, no. 3, pp. 339–350.
  13. Soldatenkov I.A. The spatial contact problem for an elastic layer and wavy punch when there is friction and wear // JAMM, 2014, vol. 78, no. 1, pp. 99–106.
  14. Goryacheva I., Yakovenko A. The periodic contact problem for spherical indenters and viscoelastic half-space // Tribol. Int., 2021, vol. 161, pp. 107078.
  15. Zolotov N.B., Pozharskii D.A. Periodic contact problems for a half-space with a partially fixed boundary // Mech. of Solids, 2022, vol. 57, no. 7, pp. 1758–1765.
  16. Galanov B.A. The method of boundary equations of the Hammerstein-type for contact problems of the theory of elasticity when the regions of contact are not known // JAMM, 1985, vol. 49, no. 5, pp. 634–640.
  17. Yakovenko A.A. Modeling of Discrete Contact of Elastic and Viscoelastic Bodies. Ph.D. Thesis. Moscow: Ishlinsky Institute for Problems in Mechanics RAS, 2022. 127 p.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2.

Download (33KB)
Indexing metadata
3.

Download (24KB)
Indexing metadata

Copyright (c) 2023 Н.Б. Золотов, Д.А. Пожарский