A novel method for concurrent dynamic topology optimization of hierarchical hybrid structures

This paper proposes a feature-decoupled method for concurrent dynamic topology optimization of the Hierarchical Hybrid Structure (HHS) to minimize the steady-state dynamic response. First, a novel single-variable uniform multiphase material interpolation model is established based on the Gaussian function and normalization method, which achieves the decoupled description of the macroscopic topology, substructure topology, and the spatial distribution of the substructures for HHS. Second, by combining the extended multiscale finite element method (EMsFEM), which overcomes the limitations of the scale separation assumption and periodic boundary conditions in HHS response analysis, a concurrent dynamic topology optimization mathematical formulation for HHS is constructed. Finally, the sensitivity scheme is established based on the adjoint method, and the MMA algorithm was employed to update the model. Numerical examples verify the correctness and feasibility of the proposed method, demonstrate its advantages in solving HHS concurrent topology optimization problem compared to traditional methods, and explore the impact of the number of substructure types on the optimization results of HHS.