Multiscale design of functionally graded cellular structures for additive manufacturing using level-set descriptions

The emergence of additive manufacturing (AM) has enabled the design of complex structures with high performance, such as functionally graded cellular structures (FGCSs). Concurrent topology optimization is commonly utilized for designing FGCSs; however, this approach suffers from an extremely high computational cost due to the complexity of the design problem. Recently, level-set-based methods, which rely on the implicit-based modeling technique, have gained increased attention and been considered as an efficient design tool for structures fabricated with AM. In this work, a multiscale structural optimization method for FGCS design utilizing level-set descriptions is proposed. Contrary to the well-known level-set topology optimization, in this approach, the shape is represented and parameterized with implicit functions, and the optimization process is performed to find the optimal parameters. The proposed method can replace topology optimization for microscale structural optimization within the multiscale structural design with reduced computation cost and comparable optimally designed results. Moreover, the unique behaviors of pre-selected cellular structures could be maintained during the optimization process by proper parametric constraints. The proposed design approach was validated through two design examples, both of which demonstrate remarkable structural performance enhancements in comparison with the single-scale design approach. Furthermore, two three-dimensional design examples, commonly found in automotive and aerospace industries, further prove the applicability of the proposed method in practice.