Functionally graded materials for prescribed field evolution

The present communication is concerned with a numerical procedure to determine an optimal material layout of a functionally graded material (FGM) within the context of a transient phenomenon. In particular, the physical problem considered here is transient heat conduction. The idea is to determine the effective material properties (via volume fraction of an isotropic composite) with the goal of controlling the evolution of the corresponding field quantity. The difference between the actual temperature field and a prescribed target field is minimized in a mean squares sense in space and time. Results show that the proposed methodology can be used for development of FGMs in a variety of practical applications.