多孔材料／结构尺度关联的一体化拓扑优化技术

INTEGRATED DESIGN OF POROUS MATERIALS AND STRUCTURES WITH SCALE-COUPLED EFFECT

针对多孔材料的尺度效应和微结构构型的可设计性,提出以宏观结构最大刚度为目标,材料表征体胞构型为变量的材料／结构尺度关联一体化设计新方法．采用有限元超单元技术,验证了材料表征体胞尺度、边长比、平移、对称周期分布方式对构型设计结果的影响,实现了材料宏观布局设计、材料表征体胞构型精细设计以及多尺度均匀化设计的统一．基于凸规划对偶优化求解技术与二次型周长控制约束,完成了快速设计与材料分布棋盘格效应的控制．计算结果表明,在给定材料用量的情况下,该方法能有效地实现蜂窝结构的拓扑优化设计,设计结果充分反映了蜂窝夹层结构的尺度效应,为轻质结构设计提供了新的设计方法．

It is known that structural behaviors of cellular sohds are dictated by the topology of the dense and porous regions, with a complex arrangement of microstructures of different sizes and topologies. In this paper, an integrated design methodology using Representative Volume Element（RVE） scale is proposed for the global stiffness maximization of the overall structure and the local design of Representative Volume Element based on multi-scale computing. Influences of Representative Volume Element aspect ratio, scale, and periodic arrangement style such as translation, symmetric pattern on the optimal design are investigated using the super-element method. By means of the dual optimization scheme and perimeter constraint, Representative Volume Elements are efficiently optimized with checkerboards being ehminated. Numerical results show that the proposed method can be used in the design of porous materials such as honeycomb panels and hierarchical cellular sandwich panels and the hierarchical cellular materials scale effects are well represented. This provides an innovative design concept for the hghtweight structures.