Multi-scale topology optimization of periodic structures with orthotropic multiple materials using the element-free Galerkin method

A multi-scale topology optimization model is proposed for orthotropic multi-material periodic structures using the element-free Galerkin method. The macro multi-material distribution is optimized with the alternating active-phase algorithm, and the effective elastic tensor of multi-type microstructures is determined by energy-based homogenization. The feasibility of the model is verified and the effects of the quantities of material types and design subdomains, the Poisson's ratio factor and the multi-material off-angle on topological configuration and compliance are studied. The results indicate that the quantity of material types affects the mechanical properties of the periodic structure, and different microstructure configurations can be obtained under different numbers of design subdomains. The increase in the Poisson's ratio factor and decrease in the off-angle can enhance the effective elastic properties of the microstructure and reduce the compliance. Reasonable values of the Poisson's ratio factor and multi-material off-angle are suggested to be 2-4 and 0-45 degrees.