Topology Optimization for Quasi-Periodic Cellular Structures Using Hybrid Moving Morphable Components and the Density Approach

Porous hierarchical structures are extensively utilized in engineering for their high specific strength, enhanced corrosion resistance, and multifunctionality. Over the past two decades, multiscale topology optimization for these structures has garnered significant attention. This paper introduces a novel hybrid MMCs (Moving Morphable Components)–density topology optimization method for quasi-periodic cellular structures. The term ‘quasi-periodic’ refers to microstructures whose different macroscopic points exhibit similar topologies with varying parameters. The primary concept involves using the MMC method to describe microstructural topology, while employing variable density to depict macro layouts. This approach leverages the advantage of MMCs in explicitly describing structural topology alongside the variable density of arbitrary microstructures. Sensitivity analyses of the optimization functions concerning design variables are shown, and a gradient optimization solver is employed to solve the optimization model. The examples effectively show the efficacy of the proposed method, illustrating that quasi-periodic cellular structures outperform single-scale solid structures.