 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 77, Issue 6 / 2013 | Next article >> |
| 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 |
04 April 2012 |
| Link to Fulltext |
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