A method of analysis for planar ideal plastic flows of anisotropic materials

The objective of the present paper is to provide an efficient method for finding steady planar ideal plastic flows of anisotropic materials. The method consists of determining two mappings between coordinate systems. One of these mappings is between principal lines-based and characteristics-based coordinate systems, and the other is between Cartesian- and characteristics-based coordinate systems. Thus, the mapping between the Cartesian- and principal lines-based coordinate systems is given in parametric form. It is shown that the boundary value problem of finding the mapping between the principal lines-based and characteristics-based coordinate systems can be reduced to the solution of a telegraph equation where two families of characteristics are curved and to the evaluation of ordinary integrals where one family of characteristics is straight. In either case, after solving this problem the problem of finding the mapping between the Cartesian- and characteristics- based coordinate systems can be reduced to the evaluation of ordinary integrals.