Mechanics

2005, No. 5

D.D. Ivlev

THE ELLIPTIC AND HYPERBOLIC WORLD

G.P. Cherepanov

ON FULL-STRENGTH TOWER

Y.N.Radayev, V.A. Gudkov

ON A NATURAL SUBALGEBRA OF THE LIE ALGEBRA OF THREE-DIMENSIONAL EQUATIONS OF THE MATHEMATICAL PLASTICITY

Group analysis of the system of partial differential equations of threedimensional plastic equilibrium is given. The Tresca yielding criterion is employed to formulate the involved system. Stress state is presumed correspond to an edge of the Tresca prism thus allowing formally consider the static equations independently on the flow rule. The system of static equilibrium equations is represented in the stress principal lines co-ordinate net (isostatic net). The symmetry group of this system is obtained. The Lie algebra and a first order optimal system of subalgebras of the symmetry group of partial differential equations of the three-dimensional mathematical theory of plasticity are studied. The optimal system which consists of 1 three-parametric, 9 two-parametric, 49 one-parametric and 87 individual elements is obtained.