This article presents a multiscale optimization method to solve size distribution problem of conformal lattice materials (CLMs). Full-scale analyses are not needed during optimization process, so this method is much more efficient compared with other optimization methods for CLMs, especially when the number of microbars is considerably large. On microscope, inherent heterogeneity of CLM makes it hard to introduce homogenization method to scale down the problem. For substitute, a new method derived from extended multiscale finite element method (EMsFEM) is used to calculate the effective stiffness of the microlattice structures, and two improvements are given to increase the accuracy and extend its application to CLM. On macroscope, based on gradient-based topology optimization method, a multiscale optimization algorithm is raised for a minimum compliance design under volume constraint. The diameters of microbars are set to be design variables. Sensitive analyses based on EMsFEM are carried out, so the effective calculating process can be seamlessly integrated in the optimization algorithm. Furthermore, considering the discontinuity of bars laid on elements’ edges, a post-processing method is proposed to determine the diameters of these bars. This optimization method is validated by two mechanical experiments on specimens fabricated by 3D printing, and its efficiency is tested by comparing with the optimization method with full-scale FE analyses. The results of both mechanical experiments and finite element simulations show that the optimized structures do have better mechanical properties, exposing the material redistribution tendency during optimizing process.

本文提出了一种多尺度优化方法来解决共形点阵材料（CLM）的尺寸分布问题。在优化过程中不需要全面分析，因此，与其他针对CLM的优化方法相比，该方法效率更高，尤其是当微棒的数量非常大时。在显微镜下，CLM固有的异质性使得难以引入均质化方法来缩小问题的范围。作为替代，使用从扩展多尺度有限元方法（EMsFEM）派生的新方法来计算微晶格结构的有效刚度，并进行了两项改进以提高精度并扩展其在CLM中的应用。在宏观上，基于基于梯度的拓扑优化方法，针对体积约束下的最小依从性设计，提出了一种多尺度优化算法。将微棒的直径设置为设计变量。进行了基于EMsFEM的敏感分析，因此可以将有效的计算过程无缝地集成到优化算法中。此外，考虑到放置在元素边缘的钢筋的不连续性，提出了一种后处理方法来确定这些钢筋的直径。通过对3D打印制成的标本进行两次机械实验，验证了该优化方法，并与全尺寸有限元分析的优化方法进行了比较，测试了该优化方法的效率。力学实验和有限元模拟的结果均表明，优化后的结构确实具有更好的力学性能，