Contact problem for an orthotropic layer with an undetermined contact zone

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Resumo

The spatial contact problem related to indenting one/two asymmetrical rigid solids into an orthotropic layer is considered. The opposite surface of the layer lies on a rigid base (friction effects of the interface are neglected). The problem is reduced to an integral equation with the kernel the principal part of which can be separated and does not contain inner integration. This part corresponds to the case of indentation into an orthotropic half-space. Under conditions of an undetermined contact area, a numerical method for nonlinear boundary integral equations is used to simultaneously determine the contact area and the contact pressure. Mechanical characteristics of the contact behavior are studied. The effect of initially discrete contact areas confluxtion for a pair of indentors located along a chosen direction is discussed.

Sobre autores

N. Zolotov

Don State Technical University

Autor responsável pela correspondência
Email: pozharda@rambler.ru
Rostov-on-Don, Russia

D. Pozharskii

Don State Technical University

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

Bibliografia

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  20. Babeshko V.A., Evdokimova O.V., Babeshko O.M. et al. On the properties of solving contact problems with friction for a punch in the form of a quarter plane in contact with a layered base // J. Appl. Math. Mech., 2025, vol. 89, no. 1, pp. 49–58. (in Russian)
  21. Ding H., Chen W., Zhang L. Elasticity of Transversely Isotropic Materials. Dordrecht: Springer, 2006. 435 p. https://doi.org/10.1007/1-4020-4034-2
  22. Fabrikant V.I. Contact and Crack Problems in Linear Elasticity. Sharjah: Bentham, 2010. 1030 p.
  23. Pan E., Chen W. Static Green’s Functions in Anisotropic Media. New York: Cambridge University Press, 2015. 356 p. https://doi.org/10.1017/CBO9781139541015
  24. Vatul’ian A.O. Contact problem with adhesion for an anisotropic layer // J. Appl. Math. Mech., 1977, vol. 41, no. 4, pp. 745–752.
  25. Vatul’yan A.O. On the rigid punch action on an orthotropic layer // Izv. Akad. Nauk Armyan. SSR. Mekh., 1978, vol. 31, no. 4, pp. 31–42. (in Russian)
  26. Vatul’yan A.O. On the rigid punch action on an anisotropic half-space // Static and Dynamic Mixed Problems of the Elasticity Theory. Rostov-on-Don: RGU Publisher, 1983, pp. 112–115. (in Russian)
  27. Pozharskii D.A. Contact problem for an orthotropic half-space // Mech. Solids, 2017, vol. 52, iss. 3, pp. 315–322. https://doi.org/10.3103/S0025654417030086
  28. Vorovich I.I., Aleksandrov V.M., Babeshko V.A. Non-classical Mixed Problems in the Elasticity Theory. Moscow: Nauka, 1974. 456 p. (in Russian)
  29. 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 // J. Appl. Math. Mech., 1985, vol. 49, no. 5, pp. 634–640. https://doi.org/10.1016/0021-8928(85)90084-X
  30. Lekhnitskii S.G. Theory of Elasticity of Anisotropic Solids. Moscow: Nauka, 1977. 416 p. (in Russian)
  31. Aleksandrov K.S., Prodaivoda G.T. Anisotropy of Elastic Properties of Minerals and Rocks. Moscow: SO RAN, 2000. 347 p. (in Russian)
  32. Huntington H. The elastic constants of crystals. II // Usp. Fiz Nauk, 1961, vol. 74, no. 3, pp. 461–520. (in Russian) https://doi.org/10.3367/UFNr.0074.196107c.0461

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