Concurrent design of hierarchical structures with three-dimensional parameterized lattice microstructures for additive manufacturing

In this work, a novel design and modeling method is proposed to obtain hierarchical structures with non-uniform lattice microstructures based on density-based topology optimization. First of all, a parametric concept is proposed to generate a family of parameterized lattice microstructures that present similar topological features. In order to balance the structural performance and computational efficiency, we construct a Parameterized Interpolation for Lattice Material (PILM) model and the mathematical formulation incorporates two new design variables. At the macroscale, the relative density variable is applied to describe material volume fraction in the design domain, instead of using the pseudo-density in the Solid Isotropic Material with Penalization (SIMP) model. At the microscale, each macroelement is regarded as an individual microstructure controlled by an aspect ratio variable. The equivalent properties of parameterized lattice microstructures can be derived by interpolating the effective elastic matrixes of several typical microstructure unit cells, which avoid expensive iterative homogenization calculations during optimization procedure. Hence, the multiscale concurrent design method can optimize the macroscopic distribution and their spatially varying microstructural configurations simultaneously at an affordable computation cost. Several numerical examples are presented to demonstrate the effectiveness of the proposed approach. Furthermore, the obtained hierarchical structures with non-uniform lattice microstructures show good manufacturability and remarkably improved structural performance by means of the additive manufacturing and experimental testing, compared to the designs with uniform lattice microstructures.