Maximizing stiffness of functionally graded materials with prescribed variation of thermal conductivity

This paper presents a computational technique for the topological design of microstructures for functionally graded materials (FGMs) with multiple graded properties of bulk modulus and thermal conductivity. The inverse homogenization method is applied for the design of a series of base cells with two constituent materials. The topology optimization of microstructures is performed by using the bi-directional evolutionary structural optimization (BESO) method, which imposes a constraint on the effective thermal conductivity. A computationally efficient approach is developed to provide smooth transition between cells by considering three cells at each stage of the optimization. Numerical examples are presented to demonstrate the effectiveness of the algorithm. The proposed approach could also be used for the design of FGMs with other functional properties.