Solutions transformation of Nadai and Prandtl for the plane ideal plasticity system

A general algorithm of transformation of the exact solutions for the plane ideal plasticity system with Mises yielding criterion by means of superposition principle is proposed. This principle is a result of infinite-dimensional symmetry group admitted by the system. As an example, the relation of Nadai solution for the converging channel and Prandtl solution for compression of a block between perfectly rough plates is considered.