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IssuesArchive of Issues2017-4pp.444-451

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K.E. Kazakov and A.V. Manzhirov, "Axisymmetric Contact between an Annular Rough Punch and a Surface Nonuniform Foundation," Mech. Solids. 52 (4), 444-451 (2017)
Year 2017 Volume 52 Number 4 Pages 444-451
DOI 10.3103/S0025654417040112
Title Axisymmetric Contact between an Annular Rough Punch and a Surface Nonuniform 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, Moscow, 105005 Russia, kazakov-ke@yandex.ru)
A.V. Manzhirov (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, Moscow, 105005 Russia; National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe sh. 31, Moscow, 115409 Russia; Moscow Technological University, pr. Vernadskogo 78, Moscow, 119454 Russia)
Abstract The axisymmetric contact problem of interaction between a two-layer foundation and a rigid annular punch is considered under the assumption that the surface nonuniformity of the upper layer and the shape of the punch base are described by rapidly varying functions. The integral equation of the problem containing two rapidly varying functions is derived, and two versions of the problem are considered. Their solutions were first constructed by the generalized projection method. As an illustration, the model problem is analyzed numerically to demonstrate the high efficiency of the method.
Keywords contact problem, rapidly varying functions, integral equation, projection method
References
1.  V. M. Alexandrov and S. M. Mkhitaryan, Contact Problems for Bodies with Thin Covers and Interlayers (Nauka, Moscow, 1983) [in Russian].
2.  A. V. Manzhirov, "Axisymmetric Contact Problems for Non-Uniformly Aging Layered Viscoelastic Foundations," Prikl. Mat. Mekh. 47 (4), 684-693 (1983) [J. Appl. Math. Mech. (Engl. Transl.) 47 (4), 558-566 (1983)].
3.  V. M. Alexandrov, "Contact Problems on Soft and Rigid Coatings of an Elastic Half-Plane," Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 42-50 (2010) [Mech. Solids (Engl. Transl.) 45 (1), 34-40 (2010)].
4.  N. F. Morozov and P. E. Tovstik, "Buckling Modes of a Compressed Plate on an Elastic Substrate," Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 30-36 (2012) [Mech. Solids (Engl. Transl.) 47 (6), 622-627 (2012)].
5.  A. V. Manzhirov, "On a Method of Solving Two-Dimensional Integral Equations of Axisymmetric Contact Problems for Bodies with Complex Rheology," Prikl. Mat. Mekh. 49 (6), 1019-1025 (1985) [J. Appl. Math. Mech. (Engl. Transl.) 49 (6), 777-782 (1985)].
6.  K. E. Kazakov, "Contact Problems for Coated Bodies," Vestnik SamGU. Estestvennonauch. Ser., No. 4, 176-196 (2007).
7.  K. E. Kazakov and A. V. Manzhirov, "Conformal Contact between Layered Foundations and Punches," Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 227-240 (2008) [Mech. Solids (Engl. Transl.) 43 (3), 512-524 (2008)].
8.  A. V. Manzhirov and K. E. Kazakov, "Contact Problem for a Foundation with a Rough Coating," Lect. Notes Eng. Comput. Sci. 2224, 877-882 (2016).
9.  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)].
10.  E. Goursat, Cours d'Analyse Mathématique, Tome III. Intégrales Infiniment Voisines; Équations aux Dérivées Partielles du Second Ordre; Équations Intégrales; Calcul des Variations (Gauthier-Villars, Paris, 1927; GTTI, Moscow-Leningrad, 1934).
11.  S. G. Mikhlin, N. F. Morozov, and M. V. Paukshto, Integral Equations in Theory of Elasticity (Izdat. St. Peterburg Univ., St. Peterburg, 1994) [in Russian].
12.  I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko, Nonclassical Mixed Problems of Elasticity (Nauka, Moscow, 1974) [in Russian].
13.  V. S. Vladimirov, Equations of Mathematical Physics (Nauka, Moscow, 1981) [in Russian].
14.  G. Szegö, Orthogonal Polynomials (Amer. Math. Soc, Providence, 1959; Fizmatgiz, Moscow, 1962).
15.  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 14 April 2017
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