Geodesic
Group analysis and exact solutions of the dynamic equations of plane strain of an incompressible nonlinearly elastic body
Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 1, pp. 11-15.

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Under study is the plane strain dynamics of an incompressible body in the framework of a nonlinear model of elasticity which uses the actual state variables. We obtain some system of nonlinear equations for displacement and pressure, give the exact solutions of the equations by using group analysis, and indicate the area of the possible application of these solutions.
Keywords: nonlinear elasticity model, group analysis
Mots-clés : invariant solutions. 
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B. D. Annin; V. D. Bondar'; S. I. Senashov. Group analysis and exact solutions of the dynamic equations of plane strain of an incompressible nonlinearly elastic body. Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 1, pp. 11-15. http://geodesic.mathdoc.fr/item/SJIM_2020_23_1_a1/

[1] I. N. Sneddon, D. S. Berry, Classical Theory of Elasticity, Springer-Verl., Berlin, 1958 | MR

[2] L. I. Sedov, Introduction to Continuum Mechanics, Fizmatgiz, M., 1962 (in Russian)

[3] L. V. Ovsyannikov, Group Analysis of Differential Equations, Nauka, M., 1978 (in Russian)

[4] B. D. Annin, V. O. Bytev, S. I. Senashov, Group Properties of Elasticity and Plasticity Equations, Nauka, Novosibirsk, 1985 (in Russian) | MR

[5] V. D. Bondar', “Dynamics of plane deformation of an incompressible nonlinearly elastic body”, Prikl. Mat. i Tekhn. Fiz., 60:4 (2019), 132–140 (in Russian) | Zbl