Optimizing a compositionally graded interlayer to reduce thermal stresses in a coated tube

We investigate the problem of optimizing the composition profile of a functionally graded interlayer inserted between a metallic tube and a ceramic coating so as to alleviate the thermal stresses occurring at the metal–ceramic interface. The optimization problem is set in the framework of optimal control and discretized using the direct transcription method. An application of the proposed approach shows (1) that as expected, functionally graded materials can be effective stress relievers by allowing gradual transitions between dissimilar materials and (2) that a stress-minimizer transition is not necessarily continuous.