Topology optimization design of multi-scale structures with alterable microstructural length-width ratios

Multi-scale topology optimization has been a hot topic during the past two decades, owing to its derived superior performances in mechanical and multi-functional properties. However, microstructural topology optimization design generally based on a prescribed rectangle design domain with a fixed micro-structural length-width ratio. In order to further extend the design space, a special composite structure with microstructures of identical topology but different length-width ratios is considered in this paper. A multi-scale topology optimization method to minimize the structural compliance by simultaneously optimizing the macrostructure, the microstructure and the microstructural length-width ratios is proposed. The mapping based asymptotic homogenization method is applied to calculate the effective material elastic matrices of the unit cells with different length-width ratios. Sensitivities of structural compliance with respect to the three types of design variables are derived and a gradient-based optimization method is applied to update the design variables. Two numerical examples are presented to verify the validity of the proposed method. Furthermore, the optimized results in the second example are manufactured by 3D printing and the experimental tests are carried out. Comparison of the stiffness performances further proves the validity of this method.