RESEARCH OF EQUATIONS DESCRIBING THE PLASTIC TORSION BARS
The article describes the equations that describe the plastic flow of prismatic bars and variable cross-section rods with a free side surface, and the rods are under pressure, varying linearly along the generator. It is shown that these equations can be reduced to a quasi-linear equations of the first order partial derivatives. Next, we study the quasi-linear partial differential equation of the first order. To this end, the general equation of the generating function found higher symmetries, depending on the independent and dependent variables, as well as derivatives of any order, built a generating function of conservation laws depending on the independent and dependent variables, as well as derivatives of any order. Studied in detail the case of practical importance when the generating function of the laws of conservation depends on the independent and dependent variables. an infinite series of conservation laws is built for the occasion. Further, the overall results are transferred to specific equations describing plastic flow, built in the first part of the article. For the equation for a prismatic rod, it shows how you can use the built conservation laws for solving boundary value problems. With their help, the coordinates of the intersection points of the characteristics found. For the rest of the equations given generating functions of conservation laws.