Optimal design and modeling of gyroid-based functionally graded cellular structures for additive manufacturing.

Lightweight cellular structure generation and topology optimization are common design methodologies in additive manufacturing. In this work, we present a novel optimization strategy for designing functionally graded cellular structures with desired mechanical properties. This approach is mainly by generating variable-density gyroid structure and then performing graded structure optimization. Firstly, the geometric properties of the original gyroid structures are analyzed, and the continuity and connectivity of the structures are optimized by adding a penalty function. Then, a homogenization method is used to obtain mechanical properties of gyroid-based cellular structures through a scaling law as a function of their relative densities. Secondly, the scaling law is added directly into the structure optimization algorithm to compute the optimal density distribution in part being optimized. Thirdly, the density mapping and interpolation approach are used to map the output of structure optimization into the parametric gyroid structure which results in an optimum lightweight lattice structure with uniformly varying densities across the design space. Lastly, the effectiveness and robustness of the optimized results are analyzed through finite element analysis and experiments.