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IssuesArchive of Issues2017-5pp.473-478

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K.E. Kazakov, "On Indentation of a System of Irregularly Shaped Rigid Punches into a Coated Foundation," Mech. Solids. 52 (5), 473-478 (2017)
Year 2017 Volume 52 Number 5 Pages 473-478
DOI 10.3103/S0025654417050016
Title On Indentation of a System of Irregularly Shaped Rigid Punches into a Coated Foundation
Author(s) K.E. Kazakov (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia; Bauman Moscow State Technical University, ul. 2-ya Baumanskaya 5 str. 1, Moscow, 105005 Russia, kazakov-ke@yandex.ru)
Abstract We consider the contact problem of interaction between a coated viscoelastic foundation and a system of rigid punches in the case where the punch shape is described by rapidly varying functions. A system of integral equations is derived, and possible versions of the statement of the problem are given. The analytic solution of the problem is constructed for one of the versions.
Keywords contact problem, rapidly varying function, system of mixed integral equations, projection method
References
1.  N. Kh. Arutyunyan and A. V. Manzhirov, Contact Problems of Creep Theory (Izdat. NAN RA, Erevan, 1999).
2.  A. V. Manzhirov, "Contact Problems of the Interaction between Viscoelastic Foundations Subjected to Ageing and Systems of Stamps not Applied Simultaneously," Prikl. Mat. Mekh. 51 (4), 670-685 (1987) [J. Appl. Math. Mech. (Engl. Transl.) 51 (4), 523-535 (1987)].
3.  A. V. Manzhirov, "Some Formulations and Solutions of Contact Problems of Creep for Arbitrary Systems of Dies," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 3, 139-151 (1987) [Mech. Solids (Engl. Transl.) 22 (3), (1987)].
4.  K. E. Kazakov, S. P. Kurdina, and A. V. Manzhirov, "Contact Interaction between Surface Inhomogeneous Foundations and Systems of Rigid Punches," Proc. IUTAM 23, 201-209 (2017).
5.  A. V. Manzhirov, S. P. Kurdina, K. E. Kazakov, and I. Fedotov, "Conformal Contact between a Viscoelastic Foundation with Rough Coating and a Finite System of Identical Rigid Punches," Vestnik Chuvash. Gos. Ped. Univ. im I. Ya. Yakovleva. Ser. Mekh. Pred. Sost., No. 4(26), 26-38 (2015).
6.  K. E. Kazakov and S. P. Kurdina, "Indentation of a Regular System of Punches into the Foundation with Rough Coating," in Mechanics for Materials and Technologies, Vol. 46: Advanced Structured Materials, Ed. by H. Altenbach, R. V. Goldstein, and E. Murashkin (Springer, 2017), pp. 297-308.
7.  V. M. Alexandrov and S. M. Mkhitaryan, Contact Problems for Bodies with Thin Coatings and Interlayers (Nauka, Moscow, 1983) [in Russian].
8.  I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko, Nonclassical Mixed Problems of Elasticity (Nauka, Moscow, 1974) [in Russian].
9.  V. S. Vladimirov, Equations of Mathematical Physics (Nauka, Moscow, 1981) [in Russian].
10.  A. V. Manzhirov, "A Mixed Integral Equation of Mechanics and a Generalized Projection Method of Its Solution," Dokl. Ross. Akad. Nauk 470 (4), 401-405 (2016) [Dokl. Phys. (Engl. Transl. 61 (10), 489-493 (2016)].
11.  A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis (Nauka, Moscow, 1976; Dover Publications, New York, 1999).
Received 23 June 2017
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