Topology optimization of microstructures of cellular materials and composites for macrostructures

This paper introduces a topology optimization algorithm for the optimal design of cellular materials and composites with periodic microstructures so that the resulting macrostructure has the maximum stiffness (or minimum mean compliance). The effective properties of the heterogeneous material are obtained through the homogenization theory, and these properties are integrated into the analysis of the macrostructure. The sensitivity analysis for the material unit cell is established for such a two-scale optimization problem. Then, a bi-directional evolutionary structural optimization (BESO) approach is developed to achieve a clear and optimized topology for the material microstructure. Several numerical examples are presented to validate the proposed optimization algorithm and a variety of anisotropic microstructures of cellular materials and composites are obtained. The various effects on the topological design of the material microstructure are discussed.