Optimization of the heating of a heat-sensitive layer under constraints on the stresses in the plastic region of deformation of the material

Abstract

We study the problem of optimal control for rapidity of the heating of a heat-sensitive layer under constraints on the control (the temperature of the heating medium or the heat flux) and maximal values of the stress intensity in the plastic region of deformation of the material. We propose an algorithm for solving the problem that presumes it has been reduced to the inverse problem of thermoplasticity. For the case of one-sided heating we give a numerical analysis of the direct and inverse problems of thermoplasticity.