 | | 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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| N.V. Banichuk, "Optimization of the contact pressure in the problem of the interaction of a punch and an elastic medium," J. Appl. Math. Mech. 74 (3), 334-340 (2010) |
| Year |
2010 |
Volume |
74 |
Issue |
3 |
Pages |
334-340 |
| Title |
Optimization of the contact pressure in the problem of the interaction of a punch and an elastic medium |
| Author(s) |
N.V. Banichuk (Moscow, Russia) |
| Abstract |
The problem of optimizing the pressure distribution under a rigid punch, which interacts without friction with an elastic medium filling a half-space, is investigated. The shape of the punch is taken as the initial variable of the design, while the root mean square deviation of the pressure distribution, which occurs under the punch, from a certain specified distribution, plays the role of the minimized functional. The values of the total forces and moments, applied to the punch, are assumed to be given, which leads to limitations imposed on the pressure distribution by the equilibrium conditions. It is shown that the optimization problem allows of decomposition into two successively solvable problems. The first problem consists of finding the pressure distribution which makes the optimized quality functional a minimum. The second problem is reduced to the problem of obtaining directly the optimum shape of the punch that yields the pressure distribution found. The optimization problem is investigated analytically for punches of different shape in plan. The optimum shapes are given in explicit form for punches with rectangular bases. |
| Received |
14 April 2009 |
| Link to Fulltext |
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