To expand the application ranges of sandwich sheets from conventional 2D flat panel types to 3D complex shapes and simultaneously improve the specific bending stiffness, a novel topology optimization strategy that can optimize the bending stiffness while maintaining good formability was proposed. In the proposed approach, the density-based topology optimization was integrated with the multi-stage genetic algorithm (GA) to optimize the repeatable unit cell of the core structure of sandwich sheets. Two optimization schemes were adopted, in which one optimizes the formability and the other one optimizes the bending stiffness while fulfilling potential failure constraints. The failure constraints on core shear failure and face buckling were theoretically deduced to mathematically formulate the topology optimization problem, which was solved by the adaptive multi-stage GA to increase the possibility of generating physically meaningful and additively manufacturable topologies. For the experimental evaluations of mechanical properties and formability, the final optimal topologies under volume fraction constraints of 50% and 62.5% were additively manufactured using carbon fibre reinforced nylon. Comparing the sandwich topologies obtained by two optimization schemes, the bending stiffness of sandwich topologies with the core density of 50% and 62.5% are improved by 41.58% and 41.49%, while the energy absorption capabilities are improved by 13.60% and 29.40% respectively. L-bending and draw-bending tests indicate the improved formability of topologically optimized sandwich sheets. The proposed approach is capable of designing formable sandwich sheets with improved bending stiffness, which is expected to expand the application envelope of sandwich sheets with better mechanical properties.

为了将夹层板的应用范围从传统的 2D 平板类型扩展到 3D 复杂形状，同时提高比弯曲刚度，提出了一种新颖的拓扑优化策略，可以在保持良好成形性的同时优化弯曲刚度。在所提出的方法中，基于密度的拓扑优化与多阶段遗传算法（GA）相结合，以优化夹芯板核心结构的可重复晶胞。采用了两种优化方案，一种优化成形性，另一种优化弯曲刚度，同时满足潜在的失效约束。理论上推导了核心剪切破坏和面屈曲的破坏约束，以数学形式表达拓扑优化问题，自适应多级 GA 解决了这个问题，以增加生成具有物理意义和可附加制造的拓扑的可能性。对于机械性能和成型性的实验评估，体积分数约束为 50% 和 62.5% 的最终最佳拓扑是使用碳纤维增强尼龙增材制造的。比较两种优化方案得到的三明治拓扑结构，芯密度为50%和62.5%的三明治拓扑结构的弯曲刚度分别提高了41.58%和41.49%，吸能能力分别提高了13.60%和29.40%。L 型弯曲和拉伸弯曲试验表明，经拓扑优化的夹层板可提高成型性。