 | | 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 |
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| In English (Mech. Solids): | | 4760 |
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| D.V. Georgievskii, "Asymptotic Integration of the Prandtl Problem in Dynamic Statement," Mech. Solids. 48 (1), 79-85 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
1 |
Pages |
79-85 |
| DOI |
10.3103/S0025654413010081 |
| Title |
Asymptotic Integration of the Prandtl Problem in Dynamic Statement |
| Author(s) |
D.V. Georgievskii (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992 Russia, georgiev@mech.math.msu.su) |
| Abstract |
The dynamic statement of the problem on the compression of a thin ideally rigid-plastic layer by absolutely rigid plates moving at constant velocities towards each other contains two characteristic dimensionless parameters. One of them-the small geometric parameter α defined as the layer thickness-to-length ratio-explicitly depends on time, and its order of smallness with respect to the other dimensionless parameter-the time-independent reciprocal Euler number-increases with time. The second parameter is assumed to be much less than unity as well. An asymptotic integration procedure is used to construct the solutions of this problem as expansions in integer powers of α; this procedure depends on the parameter ratio, i.e., is different on different time intervals. The possibility of seeking the solution in this form is justified. It is also shown that the asymptotic expansions can be matched smoothly in time.
The parameter ratio at which the correction due to inertial terms in the expression for the pressure turns out to be of the same order as the terms occurring in the classical Prandtl solution of the quasistatic problem is determined. |
| Keywords |
ideally rigid-plastic body, dynamics, Prandtl problem, spreading, compression, asymptotic expansion, Euler number |
| References |
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| 11. | D. V. Georgievskii, "Asymptotic Expansions and the Possibilities
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| 14. | D. V. Georgievskii,
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| 15. | D. V. Georgievskii,
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Zh. Prikl. Mekh. Tekhn. Fiz.
51 (5), 111-119 (2010). |
|
| Received |
03 March 2011 |
| Link to Fulltext |
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