基于复杂约束拓扑优化的负泊松比超材料设计

To solve the problems of metamaterial topology optimization design in aircraft design—being difficult to manufacture on the micro scale and non-periodic on the macro scale, a macro scale metamaterial topology optimization design method was proposed. The topological optimization design of metamaterials with prescribed Poisson’s ratio was carried out using optimality criteria and the method of moving asymptotes respectively. The negative Poisson’s ratio metamaterials satisfying the constraints in both transverse and longitudinal directions were obtained, and the design results of the two optimization algorithms were compared and analyzed. For the cell configuration obtained by topology optimization, the theoretical model and the finite element model were established, and the mechanical properties of the topology optimization results were verified. According to the calculation of the theoretical model and the finite element model, the Poisson’s ratio of the design results of topology optimization meets the design requirements. It proves the effectiveness of the macro scale topology optimization method in designing metamaterials with prescribed Poisson’s ratio.