SOLUTION OF EQUATIONS OF A PLASTIC FLOW IN CURVILINEAR COORDINATES

摘要

The plane deformation of a perfect rigtd-plastic medium is considered in curvilinear orthogonal coordinates. Methods for solving the equations of the plastic flow are considered in [1-3]. As a rule, such problems are solved in the traditional systems of coordinates-Cartesian, cylindrical or spherical. However, for metal forming, tools with more complex curved surfaces are frequently utilized and, for this reason, the development of methods for solving such problems is desired. In [4, 5], the curvilinear coordinates in which the flow lines coincide with the coordinate lines are utilized. However, it is difficult to obtain exact solutions for each of these coordinate systems. In the present paper, we consider the plane deformation in orthogonal coordinates with new functions being introduced for the coefficients of the first quadratic form and their derivatives. In some cases, this makes it possible to obtain solutions for an arbitrary orthogonal system of coordinates.