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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2011, Volume 11, Issue 2, Pages 61–77
DOI: https://doi.org/10.18500/1816-9791-2011-11-2-61-77 (Mi isu220) 		 
Mechanics

An optimal system constructing algorithm for symmetry algebra of three-dimensional equations of the perfect plasticity

V. A. Kovaleva, Yu. N. Radayevb

a Moscow City Government University of Management, Chair of Applied Mathematics
b Institute for Problems in Mechanics RAS, Moscow
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DOI: https://doi.org/10.18500/1816-9791-2011-11-2-61-77
Abstract: The present study is devoted to 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 co-ordinate net. An optimal system of one-dimensional subalgebras constructing algorithm for the Lie algebra is proposed. The optimal system (total 187 elements) is shown consist of a 3-parametrical element, twelve 2-parametrical elements, sixty six 1-parametrical elements and one hundred and eight individual elements.
Key words: theory of plasticity, isostatic co-ordinate, symmetry group, symmetry algebra, subalgebra, optimal system, algorithm.
Document Type: Article
UDC: 539.374
Language: Russian
Citation: V. A. Kovalev, Yu. N. Radayev, “An optimal system constructing algorithm for symmetry algebra of three-dimensional equations of the perfect plasticity”, Izv. Saratov Univ. Math. Mech. Inform., 11:2 (2011), 61–77
Citation in format AMSBIB
\Bibitem{KovRad11}
\by V.~A.~Kovalev, Yu.~N.~Radayev
\paper An optimal system constructing algorithm for symmetry algebra of three-dimensional equations of the perfect plasticity
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2011
\vol 11
\issue 2
\pages 61--77
\mathnet{http://mi.mathnet.ru/isu220}
\crossref{https://doi.org/10.18500/1816-9791-2011-11-2-61-77}
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    		Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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