Płaskie Stany Ośrodków Plastycznych w Nieortogonalnych Układach Współrzędnych Krzywoliniowych

The geometrical properties of non-orthogonal cylindrical curvilinear systems are used to describe plane dynamic processes and analyse general plane states of non-homogeneous rigid-plastic media without strain-hardening. The fundamental equations are expressed in a form invariant with respect to the change of the parametrization of the coordinate systems. By selecting the latter to obtain the equations in their normal form, the type of the equations set of steady, quasi-static plane flow is analysed and, in the case of the hyperbolic system, the most general form of the relations along the characteristic curves is obtained. Then, it is shown, how the relations along characteristics for the well-known cases of plane states of plastic media fallow directly
from the equations obtained.