Optimization of Thermal Treatment Modes of Bodies Made of Functionally Graded Materials

A general approach to optimal control of thermal modes of heat treatment processes of deformable elastic and viscoelastic bodies made of functionally graded materials is developed. The minimum duration of the heat treatment process is the optimality criterion at restrictions imposed on the stress–strain state of the body and the technological parameters of heating–cooling. An original method for the numerical solution of a formulated optimization problem, which, after its spatiotemporal discretization, is reduced to the parametric minimization of a function of one variable at each step in time, has been developed. Solutions to the problems of optimal control of thermal regimes in the processes of heating and cooling of finite thermosensitive cylinders made of elastic and viscoelastic functionally graded materials were obtained.