Optimizing the composition profile of a functionally graded interlayer using a direct transcription method

Abstract

We consider a three-layer cylinder consisting of a functionally graded interlayer sandwiched between a metallic layer and a ceramic layer, and address the problem of finding the interlayer composition profile minimizing the stresses resulting from material property mismatch and induced in the cylinder by temperature and pressure loading. First, we present various ways of formulating the continuous minimization problem as a thermoelastic optimal control problem, where the control is the volume fraction of either of the constituents of the interlayer, the metal or the ceramic. A direct transcription method is then used to discretize the continuous problem into a finite dimensional nonlinear optimization problem. Lastly, we present a numerical solution to the discretized problem for a specific case. Interestingly, this solution is such that the overall material distribution contains a discontinuity in volume fraction, and therefore in material properties, at the interface between the metal and the graded interlayer