Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
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IssuesArchive of Issues2016-4pp.484-493

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Total articles in the database: 9179
In Russian (. . ): 6485
In English (Mech. Solids): 2694

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Yu.E. Ivanova and V.E. Ragozina, "Solution of a Multidimensional Impact Deformation Problem for an Elastic Half-Space with Curved Boundary on the Basis of a Modified Ray Method," Mech. Solids. 51 (4), 484-493 (2016)
Year 2016 Volume 51 Number 4 Pages 484-493
DOI 10.3103/S0025654416040105
Title Solution of a Multidimensional Impact Deformation Problem for an Elastic Half-Space with Curved Boundary on the Basis of a Modified Ray Method
Author(s) Yu.E. Ivanova (Institute for Automation and Control Processes, Far East Branch of the Russian Academy of Sciences, ul. Radio 5, Vladivostok, 690041 Russia; Far East Federal University, ul. Sukhanova 8, Vladivostok, 690000 Russia,
V.E. Ragozina (Institute for Automation and Control Processes, Far East Branch of the Russian Academy of Sciences, ul. Radio 5, Vladivostok, 690041 Russia)
Abstract A generalization of the method for constructing approximate solutions of boundary value problems of impact deformation dynamics in the form of ray expansions for two-dimensional plane deformation problems is presented. For each shock wave, the solution near its front is determined on the basis of ray coordinates consistent with this wave. The nonlinear divergence of curvilinear rays is taken into account. A mechanism of transformation from one ray coordinate system to another, which is crucially important in the ray method, is described. The developed technique is illustrated by solving the impact deformation problem for a half-space with boundary of nonzero curvature.
Keywords Murnaghan model, elastic medium, shock wave, ray coordinates, nonlinear divergence of rays
1.  W. Nowacki, Theory of Elasticity (PWN, Warszawa, 1970; Mir, Moscow, 1975).
2.  A. I. Lurie, The Theory of Elasticity (Nauka, Moscow, 1970) [in Russian].
3.  D. R. Bland, Nonlinear Dynamic Elasticity (Blaisdell, London, 1969; Mir, Moscow, 1972).
4.  I. I. Goldenblat, Nonlinear Problems of Elasticity (Nauka, Moscow, 1969) [in Russian].
5.  A. G. Kulikovskii and E. I. Sveshnikov, Nonlinear Waves in Elastic Media (Moskovskii Litsei, Moscow, 1998) [in Russian].
6.  A. N. Nayfeh, Introduction to Perturbation Technique (Wiley, New York, 1981; Mir, Moscow, 1984).
7.  Yu. A. Rossikhin and M. V. Shitikova, "Ray Method for Solving Dynamic Problems Connected with the Propagation of Wave Surfaces of Strong and Weak Discontinuities," Appl. Mech. Reviews 48 (1), 1-39 (1995).
8.  L. A. Babicheva, G. I. Bykovtsev, and N. D. Verveiko, "Ray Method of Solving Dynamic Problems in Elastoviscoplastic Media," Prikl. Mat. Mekh. 37 (1), 145-155 (1973) [J. Appl. Math. Mech. (Engl. Transl.) 37 (1), 132-141 (1973)].
9.  J. D. Achenback and D. P. Reddy, "Note of Wave Propagation in Linearly Viscoelastic Media," ZAMP 18 (1), 141-144 (1967).
10.  A. A. Burenin and Yu. A. Rossikhin, "A Ray Method for Solving One-Dimensional Problems of Nonlinear Dynamic Theory of Elasticity with Plane Surfaces of Strong Discontinuities," in Applied Problems of Mechanics of Deformable Media (Izdat. DVO AN SSSR, Vladivostok, 1991), pp. 129-137 [in Russian].
11.  A. A. Burenin, "On a Possibility of Constructing Approximate Solutions of Nonstationary Problems of Dynamics of Elastic Media under Impact Actions," Dal'nevost. Mat. Sb., No. 8, 49-72 (1999).
12.  A. A. Burenin and V. E. Ragozina, "Construction of Approximate Solutions of Boundary Value Impact Strain Problems," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 101-106 (2008) [Mech. Solids (Engl. Transl.) 43 (2), 254-260 (2008)].
13.  E. A. Gerasimenko and V. E. Ragozina, "Ray Expansions in the Study of Laws of Nonplane Shock Wave Propagation," Vestnik SamGU. Estestvennonauch. Ser., No. 6/1(46), 94-113 (2006).
14.  Ye. A. Gerasimenko, A. V. Zavertan, and V. E. Ragozina, "The Use of Near-Front Ray Expansions in Deformation Dynamics," Prikl. Mat. Mekh. 73 (2), 282-288 (2009) [J. Appl. Math. Mech. (Engl. Transl.) 73 (2), 204-208 (2009)].
15.  I. V. Popov and I. V. Fryazinov, Adaptive Artificial Viscosity Method for Numerical Solution of Gas Dynamics Equations (Krasand, Moscow, 2015) [in Russian].
16.  S. K. Godunov and V. S. Ryaben'kii, Difference Schemes (Nauka, Moscow, 1973) [in Russian].
17.  T. Y. Thomas, Plastic Flow and Fracture in Solids (Academic Press, New York, 1961; Mir, Moscow, 1964).
Received 19 July 2013
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