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Procedings of the 2nd International Conference "Mathematical Physics and its Applications"
Mechanics
An optimal system of one-dimensional subalgebras for the symmetry algebra of three-dimensional equations of the perfect plasticity
V. A. Kovaleva, Yu. N. Radaevb a Dept. of Applied Mathematics, Moscow City Government University of Management Moscow
b Lab. of Modeling in Solid Mechanics,
A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, Moscow
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
The present paper is devoted to a study of a natural $12$-dimensional symmetry algebra of the three-dimensional hyperbolic differential equations of the perfect plasticity, obtained by D. D. Ivlev in 1959 and formulated in isostatic coordinates. An optimal system of one-dimensional subalgebras constructing algorithm for the Lie algebra is proposed. The optimal system (total $187$ elements) is shown consisting of of a 3-parametrical element, twelve 2-parametrical elements, sixty six 1-parametrical elements and one hundred and eight individual elements.
Keywords:
theory of plasticity, isostatic coordinate, symmetry group, symmetry algebra, subalgebra, optimal system, algorithm.
Original article submitted 20/XII/2010 revision submitted – 18/II/2011
Citation:
V. A. Kovalev, Yu. N. Radaev, “An optimal system of one-dimensional subalgebras for the symmetry algebra of three-dimensional equations of the perfect plasticity”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(22) (2011), 196–220
Linking options:
https://www.mathnet.ru/eng/vsgtu860 https://www.mathnet.ru/eng/vsgtu/v122/p196
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Abstract page: | 477 | Full-text PDF : | 227 | References: | 88 | First page: | 1 |
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