Scale separation is often assumed in most homogenization-based topology optimization (TO) frameworks for design of material microstructures. This work goes beyond the mainstream TO contributions by abandoning the scale separation hypothesis. First, it puts to evidence the limits of the homogenization-based approach when the size of the Representative Volume Element (RVE) is not negligible with respect to the structure. Then, a re-localized scheme bridging the RVE and the structure is proposed to reproduce the microscopic fields, while the structure problem at the macroscopic scale is solved only based on the coarse mesh. Finally, numerical experiments show interesting results on 2D lattice structures within the proposed framework giving a hint towards a feasible realization of the finite-scale lattice structures with current resolution of additive manufacturing technologies. Reported results evidence that the present method can lead to the same topology and stiffness of the optimized structures as the reference solution when the number of unit cell is relatively large, while reducing the computational costs significantly.

在大多数基于均质化的拓扑优化（TO）框架中，通常会假设进行尺度分离，以进行材料微结构设计。这项工作放弃了规模分离假设，超出了TO主流的贡献。首先，当代表性体积元素（RVE）的大小相对于结构不可忽略时，它证明了基于均质化方法的局限性。然后，提出了一种将RVE与结构衔接的重新定位方案，以重现微观领域，而仅基于粗糙网格来解决宏观尺度上的结构问题。最后，数值实验表明，在提出的框架内对二维晶格结构进行了有趣的研究，这为目前可行的增材制造技术分辨率的有限尺度晶格结构的实现提供了提示。报告的结果证明，当晶胞数量相对较大时，本方法可产生与参考解决方案相同的拓扑结构和优化结构的刚度，同时显着降低了计算成本。