 | | 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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| K. Yu. Osipenko and I. V. Simonov, "A model of 3D dynamics of a body of revolution interacting with low-strength media and nonsymmetric cavitation," Mech. Solids. 37 (1), 119-128 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
1 |
Pages |
119-128 |
| Title |
A model of 3D dynamics of a body of revolution interacting with low-strength media and nonsymmetric cavitation |
| Author(s) |
K. Yu. Osipenko (Moscow)
I. V. Simonov (Moscow) |
| Abstract |
An approximate mathematical model is constructed for 3D motion of a body of revolution
in a low-strength medium (of soil type) with nonsymmetric separation of flow.
We postulate a relationship between the kinematic and the load quantities
at the interface between the body and the medium. This is done in terms of
the method of an isolated element (or the method of tangential cones, as in aerodynamics,
or the method of local interaction [1, 2]) with the help of exact solutions [3, 4]
and experimental data [5, 7]. A criterion of separation is postulated for
the flow of an elastic-plastic material.
The model is reduced to a standard dynamical system by a rearrangement of variables.
The criterion of separation is used to determine the variables and the unknown boundaries
of the wetted region, which are necessary for the calculation of
the generalized forces. For elongated bodies, an asymptotically precise
analogue of autonomous equations is obtained. We also examine the region
of separation and find the conditions of stability of rectilinear motion of
thin bodies.
Previously, one-dimensional cavity motion of bodies was studied in [8-10].
Numerical analysis of plane-parallel motion of projectiles in soil is given in [11].
The first integrals for the problem of 3D motion of a body in viscous fluid
are constructed in [12] under the assumption that the interaction
of the body and the fluid is limited to its disk-shaped front piece [12].
Some recent publications propose new technologies based on
deep penetration of projectiles. In particular, probes are being
developed for exploring physical and chemical properties of structures on
the surface of other planets [13], and there are some proposals
regarding control of volcanic and seismic activities [14]. On the other
hand, experiments with penetration of various media by projectiles often
demonstrate a distortion of the trajectory of motion in the presence of
nonsymmetric cavitation (sometimes, the trajectory has the form of a loop
and the projectile moves out of the target, having turned around by 180°). In this connection, it is especially important to analyze
numerically deep penetration, shape optimization, and stability of motion
of a body in a medium with high strength characteristics.
However, when formulated precisely, such problems can hardly be solved at all [8].
The advanced numerical methods applied to these problems are effective only
at the early stages of impact, whereas the results of long-term
calculations may be erroneous. Moreover, since there are many parameters
and determining functions, calculations do not allow us to identify the
general laws of the penetration process.
It has often been said that the instability of the dynamic properties of
soils and other porous materials reduces the requirements for the precision
of the models. Therefore, the utilization of approximate
methods reducing the original problem to the classical
dynamic problem for a solid body by means of a phenomenological description
of the medium-body interaction and calibration of the model on the
experimental basis [8-12] would be justified. |
| References |
| 1. | A. Ya. Sagomonyan, Penetration [in Russian], Izd-vo MGU, Moscow, 1974. |
| 2. | A. Ya. Sagomonyan, "Breaking through slabs by thin solid
projectiles," Vestnik MGU [Bulletin of Moscow State University], Ser. 1,
Mat., Mekh., No. 5, pp. 104-111, 1975. |
| 3. | L. M. Flitman, "Subsonic axially symmetric flow of
elastic-plastic media past thin pointed bodies of revolution," Izv. AN
SSSR. MTT [Mechanics of Solids], No. 4, pp. 155-164, 1991. |
| 4. | L. M. Flitman,
"High-speed elastic-plastic flow without separation past blunt-nosed
bodies," PMM [Applied Mathematics and Mechanics], Vol. 54, No. 4,
pp. 642-651, 1990. |
| 5. | Yu. K. Bivin, V. V. Viktorov, and B. Ya. Kovalenko,
"Determination of dynamic characteristics of soils by penetration,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 3, pp. 105-110, 1980. |
| 6. | Yu. K. Bivin, V. A. Kolesnikov, and L. M. Flitman,
"Determination of mechanical properties of media by the method of dynamic
penetration," Izv. AN SSSR. MTT [Mechanics of Solids], No. 5,
pp. 181-184, 1982. |
| 7. | Yu. K. Bivin,
"Cavity formation for vertical penetration of elastic-plastic medium
by solid bodies," Izv. AN. MTT [Mechanics of Solids], No. 1,
pp. 93-101, 1997. |
| 8. | S. S. Grigoryan, "An approximate solution of a problem of
soil penetration," Izv. AN. MZhG [Fluid Dynamics], No. 4, pp. 18-24,
1993. |
| 9. | Yu. K. Bivin and I. V. Simonov,
"Estimates of penetration depths for solid bodies entering soil
at supersonic velocities," Doklady AN, Vol. 328, No. 4, pp. 447-450,
1993. |
| 10. | I. V. Simonov, "Cavitational penetration of a strong medium
by bodies of minimal resistance," PMM [Applied Mathematics and Mechanics],
Vol. 57, No. 6, pp. 110-119, 1993. |
| 11. | V. A. Veldanov, A. L. Isaev, D. V. Marinchev, and Yu. M. Pushilin,
"A computer program for the calculation of the parameters
of obstacle-projectile interaction process," in
Numerical Methods in Problems of Elasticity and Plasticity.
Proceedings of the 12-th All-Union Conference. Tver, 1991 [in Russian], pp. 65-72,
Izd-vo ITPM SO RAN, Novosibirsk, 1992. |
| 12. | M. V. Shamolin,
"On an integrable case in the 3D dynamics of solid bodies interacting with
media," Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 65-68, 1997. |
| 13. | A. V. Bogdanov, A. V. Nikolaev, V. I. Serbin, G. A. Skuridin,
O. B. Khavroshkin, and O. B. Tsyplakov, "A method for the exploration
of Earth-type planets," Kosmicheskie Issledovaniya [Space Research],
Vol. 26, No. 4, pp.591-603, 1988. |
| 14. | I. V. Simonov, S. A. Fedotov, and O. B. Khavroshkin,
"Precatastrophic state of geophysical objects, triggering control
and penetration," Doklady AN, Vol. 347, No. 6, pp. 811-813, 1996. |
| 15. | I. V. Simonov,
"Transonic flow of elastic medium past a thin solid body,"
PMM [Applied Mathematics and Mechanics], Vol. 48, No. 1, pp. 114-122, 1984. |
| 16. | S. k. Betyaev, "Hydrodynamics: problems and paradoxes,"
Uspekhi Fiz. Nauk, Vol. 165, No. 3, pp. 299-330, 1995. |
| 17. | Yu. K. Bivin, Yu. M. Glukhov, Yu. V. Permyakov,
"Vertical penetration of water by rigid bodies,"
Izv. AN SSSR. MZhG [Fluid Dynamics], No. 6, pp. 3-9, 1985. |
| 18. | K. Yu. Osipenko and I. V. Simonov, "Supersonic flow
of a porous medium past a cone," Izv. AN. MTT [Mechanics of Solids],
No. 2, pp. 87-96, 2001. |
| 19. | J. Poncelet, "Rapport sur un Mèmoire de MM Piobern et Morin,
concernant les expériences faites à Metz en 1834, sur la
énétration des projectiles dans milieux resistants et sur la rupture de
corps par le choc," Mem. Acad. Sci. Paris, Vol. 15, pp. 55-91, 1838. |
| 20. | I. V. Simonov,
"On the stability of motion of an elongated body of revolution
in elastic-plastic medium with flow separation," PMM [Applied Mathematics
and Mechanics], Vol. 64, No. 2, pp. 311-320, 2000. |
|
| Received |
23 November 1999 |
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