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Russian Academy of Sciences
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(Translated from 1958)
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IssuesArchive of Issues2013-6pp.642-658

Archive of Issues

Total articles in the database: 1813
In Russian (): 1014
In English (J. Appl. Math. Mech.): 799

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V.B. Zelentsov, "The dynamics of the motion of a flat punch on the boundary of an elastic half-plane," J. Appl. Math. Mech. 77 (6), 642-658 (2013)
Year 2013 Volume 77 Issue 6 Pages 642-658
Title The dynamics of the motion of a flat punch on the boundary of an elastic half-plane
Author(s) V.B. Zelentsov (Don State Technical University, Rostov-on-Don, Russia, vbzelen@gmail.com)
Abstract The dynamic contact problem of the motion of a flat punch on the boundary of an elastic half-plane is considered. During motion, the punch deforms the elastic half-plane, penetrating it in such a manner that its base remains parallel to the boundary of the half-plane at each instant of time. In movable coordinates connected to the moving punch, the contact problem reduces to solving a two-dimensional integral equation, whose two-dimensional kernel depends on the difference between the arguments for each of the variables. An approximate solution of the integral equation of the problem is constructed in the form of a Neumann series, whose zeroth term is represented in the form of the superposition of the solutions of two-dimensional integral equations on the coordinate semiaxis minus the solution of the integral equation on the entire axis. This approach provides a way to construct the solution of the two-dimensional integral equation of the problem in four velocity ranges of motion of the punch, which cover the entire spectrum of its velocities, as well as to perform a detailed analysis of the special features of the contact stresses and vertical displacements of the free surface on the boundary of the contract area. An approximate method for solving the integral equation, which is based on a special approximation of the integrand of the kernel of the integral equation in the complex plane, is proposed for obtaining effective solutions of the problem that do not contain singular quadratures.
Received 4 April 2012
Link to Fulltext http://www.sciencedirect.com/science/article/pii/S0021892814000197
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