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.], 2011, Issue 1(22),Pages <nobr>196

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. Kovalev^a, Yu. N. Radaev^b

^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

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.

UDC: 539.3

MSC: 74C05

Original article submitted 20/XII/2010
revision submitted – 18/II/2011

DOI: 10.14498/vsgtu860