Optimal control and optimization of functionally graded materials for thermomechanical processes

The present communication is concerned with the control and/or optimization of a two-phase isotropic composite under time-dependent thermomechanical loadings. A control-like problem and a structural optimization problem are formulated using a common framework. In both cases the material properties are used as primary design variables and no a priori assumptions are made regarding the spatial distribution of each phase. For optimal control problems, the objective is to minimize the difference between field variables and target fields and for structural optimization problems the objective is to minimize the product of conjugate thermodynamical variables. Within this context, it is shown that for the minimum structural compliance problem, the optimal distribution of material properties depends on the loading history, even though the deformations are elastic. For a simplified thermal barrier design, it is shown that the problem requires simultaneous control of stresses and thermal energy via a multi-objective formulation