A Hybrid Level Set Optimization Design Method of Functionally Graded Cellular Structures Considering Connectivity

With the continuous advancement in topology optimization and additive manufacturing (AM) technology, the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying microstructures has grown significantly. However, a critical challenge is encountered in the design of these structures–the absence of robust interface connections between adjacent microstructures, potentially resulting in diminished efficiency or macroscopic failure. A Hybrid Level Set Method (HLSM) is proposed, specifically designed to enhance connectivity among non-uniform microstructures, contributing to the design of functionally graded cellular structures. The HLSM introduces a pioneering algorithm for effectively blending heterogeneous microstructure interfaces. Initially, an interpolation algorithm is presented to construct transition microstructures seamlessly connected on both sides. Subsequently, the algorithm enables the morphing of non-uniform unit cells to seamlessly adapt to interconnected adjacent microstructures. The method, seamlessly integrated into a multi-scale topology optimization framework using the level set method, exhibits its efficacy through numerical examples, showcasing its prowess in optimizing 2D and 3D functionally graded materials (FGM) and multi-scale topology optimization. In essence, the pressing issue of interface connections in complex structure design is not only addressed but also a robust methodology is introduced, substantiated by numerical evidence, advancing optimization capabilities in the realm of functionally graded materials and cellular structures.