Multi-Material Optimization for Lattice Materials Based on Nash Equilibrium

Lattice materials are regarded as a new family of promising materials with high specific strength and low density. However, in the optimization of lattice materials, it is difficult in general to determine the material distribution in lattice structures due to the complex optimization formulations and overlaps between different materials. Thus, the article proposes to use the Nash equilibrium to address the multi-material optimization problem. Moreover, a suppression formula is investigated to tackle the issue of material overlapping. The proposed method is validated using a cantilever beam example, showing superior optimization results compared to single-material methods, with a maximum improvement of 20.5%. Moreover, the feasibility and stability of the approach are evaluated through L-shaped beam examples, demonstrating its capability to effectively allocate materials based on their properties and associated stress conditions within the design. Additionally, an MBB test demonstrates superior stiffness in the proposed optimized specimen compared to the unoptimized one.