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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. B. Zelentsov and N. Yu. Baturina, “Dynamics of Plane Punch Penetration into a Horizontally Shifted Elastic Half-Plane,” in Contemporary Problems ofMechanics (Novocherkassk, 2011), pp. 71–74 [in Russian].
V. M. Alexandrov and E. V. Kovalenko, Problems with Mixed Boundary Conditions in Continuum Mechanics (Nauka, Moscow, 1986) [in Russian].
A. V. Belokon’ and A. V. Nasedkin, “Interaction of Moving Punches with Elastic and Viscoelastic Bodies,” inMechanics of Contact Interactions (Fizmatlit, Moscow, 2001), pp. 331–348 [in Russian].
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)].
I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko, Nonclassical Mixed Problems of Elasticity (Nauka, Moscow, 1974) [in Russian].
V. B. Zelentsov, “The Impact of a Plane Punch on an ElasticHalf-Plane,” Prikl.Mat. Mekh. 70(1), 150–161 (2006) [J. Appl.Math. Mech. (Engl. Transl.) 70 (1), 139–149 (2006)].
B. Noble, Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations (Pergamon Press, London etc., 1958;Mir, Moscow, 1962).
V. B. Poruchikov,Methods of Dynamic Elasticity (Nauka, Moscow, 1986) [in Russian].
N. Ya. Vilenkin, E. A. Gorin, A. G. Kostyuchenko, et al., Functional Analysis (Nauka, Moscow, 1964) [in Russian].
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).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.B. Zelentsov, R.V. Sakhabudinov, 2014, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2014, No. 2, pp. 112–123.
About this article
Cite this article
Zelentsov, V.B., Sakhabudinov, R.V. Uniform motion of a plane punch on the boundary of an elastic half-plane. Mech. Solids 49, 208–217 (2014). https://doi.org/10.3103/S0025654414020101
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0025654414020101