Пространственная задача математической теории пластичности. Радаев Ю.Н. - 459 стр.

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principal lines co-ordinate 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 consists of 1 three-parametric, 9 two-parametric, 45 one-parametric

and 95 individual elements. By the Lie technique new exact solutions are obtained in

analytically closed forms for the axially-symmetric problem. Some of them are represented

by the canonical Legendre elliptic integrals. A number of self-similar solutions of the axially

symmetric problem is given by introducing a self-similar variable as the products of powers of

the isostatic co-ordinates. For special values of parameters involved in the self-similar solution

the problem is reduced to obtaining solution of a non-linear non-autonomous ordinary

diﬀerential equation. Then this equation is numerically analyzed. The computation of principal

stresses distributions within the self-similar solutions zone is implemented.

Ю.Н. Радаев