Optimal heating control of thermosensitive bodies under plastic deformation of material

A mathematical statement has been formulated and algorithms for solving one- and two-dimensional problems on fast operation optimal heating control of homogeneous thermosensitive canonical form bodies has been developed. We have determined the control (the surrounding temperature at one of the boundary surfaces or heat flux at one of the boundary surfaces) which in a minimal time carries the body from the initial thermal state to the final one, characterized by the given mean-integral temperature. In addition, restrictions on the control function and the maximal tangential stress intensity or accumulated plastic shear strain have been considered. The elastoplastic deformation of the material has been studied within the framework of general plasticity theory proposed by Il'yushin.