A Superposition of the Nadai and Prandtl Solutions to the Two-Dimensional Ideal Plasticity System

We give a general algorithm for transforming exact solutions to the flat ideal plasticity system of Mises using the superposition principle for solutions, which arises as a corollary to the original system admitting an infinite dimensional symmetry group. As an example we consider a relation between the known exact solutions: the Prandtl solution for a thin layer compressed by rough solid plates, and the Nadai solution for the radial distribution of stresses in a convergent channel in the shape of a flat wedge.