Functionally Graded Materials (FGMs) have a gradual material variation from one material character to another throughout the structure. Applications of these types of materials have significant advantages in civil and mechanical systems including thermal systems. Analyzing the FGMs at the microstructure level with the conventional Finite Element Method (FEM) takes enormous pre-processing and computational time due to the complex material characteristics at the microstructure level. Essentially, the model contains too many degrees of freedom to be solved economically.