Optimization of temperature-dependent functionally graded material bodies

We consider thermoelastic bodies composed of two-constituent functionally graded materials under steady-state conditions and address the problem of the optimal choice of composition profile. First, we formulate the problem as a partial-differential-equation constrained optimization problem, where the control function is the composition profile. The formulation includes the temperature-dependence of the constituents’ properties. Next, we derive the objective functional gradient using the continuous adjoint-field approach. Lastly, we use the gradient information into a gradient-based algorithm to optimize a thick-walled functionally graded sphere subjected to thermal gradients. For the numerical data we use, the optimal composition profile obtained is such that in the graded sphere the maximum von Mises stress, here used as a performance index, is about half that in the homogeneous sphere composed of either constituent.