Reproduction of solutions of bidimensional ideal plasticity

The symmetries of a system of differential equations allowed the transformation of its solutions to a solution of this system. New analytical exact solutions of a system of two-dimensional ideal plasticity equations were constructed from two well-known solutions, that for a circular cavity stressed by normal pressure, and Prandtl's solution for a block compressed between perfectly rough plates, for the case where the thickness of the block was rather small. A mechanical sense of new solutions was discussed.