Topology optimization of functionally graded lattice structure with machine learning

Abstract

Lattice structures are arrangements where identical or similar patterns repeat throughout the design space, offering excellent physical and material properties such as lightweight, energy absorption, and noise reduction. Functionally graded lattice structures can perform better than uniform lattice structures by adjusting the lattice structure and material distribution for different situations to optimize mechanical properties such as stiffness and strength. Various studies are underway to design these functionally graded lattice structures. However, the numerical analysis required for designing functionally graded lattice structures can be computationally expensive due to the complex geometric shapes of the microstructures and the large number of design variables involved. To address this, the homogenization method was applied, which replaced the complex shapes and properties of the microstructures with equivalent homogenized unit cells. Homogenization uses effective properties to reduce numerical analysis costs instead of directly analyzing the various lattice shapes determined by the changing design variables. In this study, topology optimization based on homogenization was used to design functionally graded lattice structures. As the variables defining the functionally graded lattice structure increase, it becomes easier to search for structures optimized for material distribution and specific uses. However, this increases the complexity of data configuration and the difficulty in developing models to express the material properties. Therefore, instead of polynomial-based surrogate models, a machine learning-based surrogate model was utilized, which uses design variables as input and effective properties as output. The computational cost of homogenization, performed through finite element analysis, increases exponentially with the increase in design variables. To obtain information on the design variable space with minimal analysis, sampling based on the Design of Experiments was used to generate training data for the machine learning model. Numerical examples that maximized the structural stiffness under given loads were conducted to demonstrate the effectiveness of the proposed method. The optimized distribution of design variables from topology optimization was used to restore the microstructure of the functionally graded lattice structure through the process of de-homogenization. The results were compared with uniform lattice structures to confirm the superiority of the functionally graded lattice structures. The results obtained from topology optimization were manufactured using additive manufacturing techniques.