Two-scale concurrent topology optimization of lattice structures with multiple microstructures subjected to dynamic load

This work intends to present a two-scale concurrent topology optimization method for minimizing the compliance of lattice structures with multiple connectable microstructures under time-dependent dynamic load. Firstly, at the macroscale, the ordered solid isotropic material with penalization (SIMP) method and double smoothing and projection method is integrated to identify the macrostructural layout of any lattice material represented by a unique microstructure, i.e. optimal locations of microstructures. At the microscale, the connectivity between any pair of microstructures is guaranteed by adopting the designable connective region method. Then, for transient optimization problem, we implement the sensitivity analysis based on the adjoint method with the "discretize-then-differentiate" approach, which inherently generates consistent sensitivities. Moreover, we develop a decoupled sensitivity analysis method for transient concurrent topology optimization problems with multiple connectable microstructures for computationally efficient sensitivity analysis at the microscale. Finally, several numerical examples are presented to verify the effectiveness and the capability of the proposed approach.