Concurrent topology optimization design of structures and non-uniform parameterized lattice microstructures

This paper presents a novel concurrent topology optimization approach for finding the optimum topologies of macrostructures and their corresponding parameterized lattice microstructures in an integrated manner. Considering the manufacturability of the structure designs and computational efficiency, additional parameters are introduced to define the microstructure unit cell patterns and their non-uniform distribution, which avoids expensive iterative numerical homogenization calculations during topology optimization and results in an easier modelling of structure designs as well. It is worth mentioning that the equivalent properties of material microstructures serve as a link between the macro and the micro scale with the help of homogenization theory and the Porous Anisotropic Material with Penalization (PAMP) model. Besides, sensitivities of global structure compliance with respect to the pseudo-density variables and the microstructure parameter variables are derived, respectively. Moreover, several numerical examples are presented and reasonable solutions have been obtained to demonstrate the efficiency of the proposed method. Finally, mechanical testing is conducted to investigate the better performance of the optimized structure which is fabricated by 3D printing.