This paper performs a combined numerical and experimental study to explore the role of minimum length scale constraints in multi-scale topology optimisation. Multi-scale topology optimisation is generally performed without considering the actual unit cell size, while an arbitrary value considerably smaller than the part is selected afterwards. However, this procedure would be problematic if including geometric constraints, e.g. minimum length scale constraints, since geometric constraints cannot be applied without knowing the unit cell dimensions. To address this issue, unit cell size should be defined beforehand, and guidelines will be provided in this work through a thorough numerical exploration, i.e. compliance minimisation multi-scale topology optimisation with different unit cell sizes and a consistent minimum length scale limit will be performed. The numerical results indicate that selecting the unit cell size considerably smaller than the part and larger than the length scale limit would be recommended. Then, experiments are conducted to explore the effect of minimum length scale limit on the stiffness and strength of the multi-scale design. It is observed that increasing the minimum length scale limit would reduce the structural mechanical performance in both aspects.

本文进行了数值和实验相结合的研究，以探索最小长度尺度约束在多尺度拓扑优化中的作用。通常在不考虑实际单位像元大小的情况下执行多尺度拓扑优化，然后选择比该零件小得多的任意值。然而，如果包括几何约束，例如最小长度尺度约束，则该过程将是有问题的，因为在不知道单位晶胞尺寸的情况下不能施加几何约束。为了解决这个问题，应预先定义晶胞大小，并通过全面的数值探索在这项工作中提供指导，即 将执行具有不同单位像元大小和一致的最小长度尺度限制的合规性最小化多尺度拓扑优化。数值结果表明，建议选择单位体积明显小于零件尺寸且大于长度比例尺极限的尺寸。然后，进行实验以探索最小长度比例限制对多比例设计的刚度和强度的影响。可以看出，增加最小长度比例尺极限会降低这两个方面的结构机械性能。进行实验以探索最小长度比例尺限制对多比例尺设计的刚度和强度的影响。可以看出，增加最小长度比例尺极限会降低这两个方面的结构机械性能。进行实验以探索最小长度比例尺限制对多比例尺设计的刚度和强度的影响。可以看出，增加最小长度比例尺极限会降低两个方面的结构机械性能。