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Dombrovskij, G. A.; Turchenko, V. Ya.

Exact solutions of the equations of one-dimensional nonstationary motions of nonlinearly elastic media. (English) Zbl 0416.73047

Sov. Appl. Mech. 12, 399-405 (1976).
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MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
35Q99 Partial differential equations of mathematical physics and other areas of application
74J99 Waves in solid mechanics
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)

Keywords:

exact solutions; one-dimensional nonstationary motions; nonlinearly elastic media; longitudinal shock loading; thin rod; finite length

Citations:

Zbl 0342.73041
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Full Text: DOI

References:

[1] G. A. Dombrovskii, ?On the approximate integration of the equations of the supersonic flow of a gas,? in: (edited by L. I. Sedov), Theoretical Hydromechanics [in Russian], No. 3, Moscow (1953), pp. 105?114.
[2] G. A. Dombrovskii, ?Approximate integration of the equations of one-dimensional nonstationary motion of a gas,? Izv. Akad. Nauk SSSR, Mekh. Mashinostr., No. 6, 111?115 (1963).
[3] G. A. Dombrovskii, Methods of Approximations of an Adiabat in the Theory of Two-Dimensional Flows of a Gas [in Russian], Nauka, Moscow (1964).
[4] G. A. Dombrovskii, ?On certain transformations of systems of equations of the Chaplygin type,? in: Materials of the Conference on Boundary-Value Problems [in Russian], Kazan’ (1970), pp. 94?97.
[5] G. A. Dombrovskii, G. V. Litvinov, and B. M. Malyshev, ?Longitudinal shock stretching of a tight wire,? Inzh. Zh., Mekh. Tverd. Tela, No. 2, 106?110 (1968).
[6] G. I. Nazarov and N. G. Puchkova, ?Use of an approximation method in magnetohydrodynamics to calculate the efflux from a container with a nozzle,? in: Some Problems of Aerodynamics and Electrodynamics [in Russian], No. 6, Kiev (1970), pp. 137?145.
[7] V. Ya. Turchenko, ?Application of the Legendre transformation to the study of plane elastoplastic stress waves,? Inzh. Zh., Mekh. Tverd. Tela, No. 4, 166?170 (1968).
[8] V. M. Fomin, ?Exact solutions of certain problems of nonlinear electrodynamics,? Zh. Tekh. Fiz.,39, No. 4, 593?501 (1969).
[9] I. M. Yur’ev, ?on the linearized theory of the supersonic flow of a gas around bodies of revolution,? Prikl. Mat. Mekh.,19, No. 3, 363?367 (1955).
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