 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| N.V. Banichuk and S.Yu. Ivanova, "Determination of Optimal Shape of a Moving Punch with Friction Taken into Account," Mech. Solids. 47 (5), 591-597 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
5 |
Pages |
591-597 |
| DOI |
10.3103/S0025654412050135 |
| Title |
Determination of Optimal Shape of a Moving Punch with Friction Taken into Account |
| Author(s) |
N.V. Banichuk (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, banichuk@ipmnet.ru)
S.Yu. Ivanova (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, ivanova@ipmnet.ru) |
| Abstract |
The optimization problem for the contact interaction between a rigid punch and an elastic medium is considered. It is assumed that that the punch is under the action of some prescribed forces and momenta and moves along a surface bounding a half-space filled with an elastic medium. It is also assumed that the motion is quasistatic and the friction forces arising in the region of contact are taken into account. The punch shape is considered as the desired design variable, and the integral functional characterizing the discrepancy between the pressure distribution in the region of contact that corresponds to the optimized shape of the punch and a given goal distribution of pressure is taken as the minimizing criterion. The optimal shape can be determined efficiently by solving the following two problems: first, to obtain the optimal pressure distribution and then to solve a boundary value problem for the elastic half-space under the action of the obtained normal pressure and friction forces. By way of example, the optimal shape is analytically determined for a punch of rectangular shape in horizontal projection. |
| Keywords |
moving punch, shape optimization, contact pressure, friction taken into account |
| References |
| 1. | I. G. Goryacheva,
Mechanics of Friction Interaction
(Nauka, Moscow, 2001)
[in Russian]. |
| 2. | N. V. Banichuk, S. Yu. Ivanova, and E. V. Makeev,
"Reliable Optimal Design in Contact Mechanics,"
in Recent Advances in Mechanics. Selected Papers from the Symposium on Recent Advances in Mechanics, Academy of Athens, Athens, Greece, 2009,
Ed. by A. N. Kounadis at al.
(Springer Science+Business Media B.V., 2011), pp. 27-42. |
| 3. | A. I. Lurie,
Spatial Problems of Theory of Elasticity
(Gostekhizdat, Moscow, 1955)
[in Russian]. |
| 4. | A. E. H. Love,
A Treatise on the Mathematical Theory of Elasticity
(Dover, New York, 1944). |
|
| Received |
12 May 2011 |
| Link to Fulltext |
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