The method of characteristics in ideal plasticity problems

A universal computer algorithm and computer program is developed that implements a direct version of the method of characteristics for solving systems of quasilinear first-order partial differential equations in two independent variables. The algorithm is used to calculate the lattice of slip lines and the velocity vector field in problems of the limiting equilibrium of ideally plastic and friable media. Results of the numerical solution of an ideal plasticity problem for a plane with an aperture loaded with an internal pressure, of the plane problem of the limiting equilibrium of a friable medium and of the axisymmetric problem of a rotating punch on the surface of a plastic half-space are presented to demonstrate the efficiency of the method.