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IssuesArchive of Issues2014-2pp.208-217

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V.B. Zelentsov and R.V. Sakhabudinov, "Uniform Motion of a Plane Punch on the Boundary of an Elastic Half-Plane," Mech. Solids. 49 (2), 208-217 (2014)
Year 2014 Volume 49 Number 2 Pages 208-217
DOI 10.3103/S0025654414020101
Title Uniform Motion of a Plane Punch on the Boundary of an Elastic Half-Plane
Author(s) V.B. Zelentsov (Vorovich Research Institute of Mechanics and Applied Mathematics, South Federal University, pr-t Stachki 200/1, Rostov-on-Don, 344090 Russia, vbzelen@gmail.com)
R.V. Sakhabudinov (4th Central Scientific Research Institute, Ministry of Defence of the Russian Federation, Tikhonravova 29, Yubileynyy, Moscow Oblast, 141080 Russia, cnii4@yandex.ru)
Abstract The dynamic contact problem of a plane punch motion on the boundary of an elastic half-plane is considered. The punch velocity is constant and does not exceed the Rayleigh wave velocity. The moving punch deforms the elastic half-plane penetrating into it so that the punch base remains parallel to itself at all times. The contact problem is reduced to solving a two-dimensional integral equation for the contact stresses whose two-dimensional kernel depends on the difference of arguments in each variable. A special approximation to the kernel is used to obtain effective solutions of the integral equation. All basic characteristics of the problem including the force of the punch elastic action on the elastic half-plane and the moment stabilizing the punch in the horizontal position in the process of penetration are obtained. A similar problem was considered in [1] and earlier in the "mode of steady-state motions" in [2, 3] and in other publications.
Keywords punch, half-plane, penetration, nonstationary contact problem, two-dimensional integral equation, kernel
References
1.  V. B. Zelentsov and N. Yu. Baturina, "Dynamics of Plane Punch Penetration into a Horizontally Shifted Elastic Half-Plane," in Contemporary Problems of Mechanics (Novocherkassk, 2011), pp. 71-74 [in Russian].
2.  V. M. Alexandrov and E. V. Kovalenko, Problems with Mixed Boundary Conditions in Continuum Mechanics (Nauka, Moscow, 1986) [in Russian].
3.  A. V. Belokon' and A. V. Nasedkin, "Interaction of Moving Punches with Elastic and Viscoelastic Bodies," in Mechanics of Contact Interactions (Fizmatlit, Moscow, 2001), pp. 331-348 [in Russian].
4.  L. M. Flitman, "Dynamic Problem of the Die on an Elastic Half-Plane," Prikl. Mat. Mekh. 23 (4), 697-705 (1959) [J. Appl. Math. Mech. (Engl. Transl.) 23 (4), 997-1008 (1959)].
5.  I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko, Nonclassical Mixed Problems of Elasticity (Nauka, Moscow, 1974) [in Russian].
6.  V. B. Zelentsov, "The Impact of a Plane Punch on an Elastic Half-Plane," Prikl. Mat. Mekh. 70 (1), 150-161 (2006) [J. Appl. Math. Mech. (Engl. Transl.) 70 (1), 139-149 (2006)].
7.  B. Noble, Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations (Pergamon Press, London etc., 1958; Mir, Moscow, 1962).
8.  V. B. Poruchikov, Methods of Dynamic Elasticity (Nauka, Moscow, 1986) [in Russian].
9.  N. Ya. Vilenkin, E. A. Gorin, A. G. Kostyuchenko, et al., Functional Analysis (Nauka, Moscow, 1964) [in Russian].
10.  V. B. Zelentsov, "On Impact of a Parabolic Punch on an Elastic Half-Plane," Izv. Vyssh. Uchebn. Zaved. Sev.-Kavkaz. Region, No. 1, 27-33 (2011).
Received 10 August 2011
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