Topology optimization of functionally graded cellular materials

Design of functionally graded material (FGM), in which the mechanical property varies along one direction, is the focus of this study. It is assumed that the microstructure of the FGM is composed of a series of base cells in the variation direction and self-repeated in other directions. Bi-directional evolutionary structural optimization technique in the form of inverse homogenization is used for the design of the FGM for specified variation in bulk or shear modulus. Instead of designing a series of base cells simultaneously, the base cells are optimized progressively by considering three base cells at each stage. Thus, the proper connections between adjacent base cells can be achieved with high computational efficiency. Numerical examples demonstrate the effectiveness of the proposed method for designing microstructures of 2D and 3D FGMs with specified variation in bulk or shear modulus. The proposed algorithm can also be easily extended to design FGMs with other functional properties.