Variational methods in the mechanics of metal forming by pressure

The strain state and forces at upsetting of an ingot, forging of a strip etc. are investigated on the basis of the minimum total power principle. Applied problems are solved with the use of direct methods. More precise and flexible is the method of reduction to ordinary differential equations. Unknown functions of a single co-ordinate are determined by solving of the system of Euler's equations for the energy functional. This approach is used for the spatial problem of investigation of the strain state of a high parallelepiped under compression.