Scale separation is often assumed in most multiscale topology optimization frameworks. In this work, topology optimization of heterogeneous structures consisting of inseparable unit cells is studied. The cell morphology is given first and remains unchanged during the optimization process. A nonlocal numerical homogenization method is used to construct a mesoscopic constitutive relationship between the material and the structural scales. Topology optimization is performed on heterostructures at the higher mesoscale, and only based on a coarse grid for computational savings. Numerical studies show that the structural stiffness has been significantly improved compared to classical multiscale topology optimization using separation assumptions. However, there is still a size dependence of the optimal mesostructure related to the characteristic effect of the unit lattice.

中文翻译：

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非分离尺度的异质介观结构设计和尺寸效应分析

在大多数多尺度拓扑优化框架中经常假定尺度分离。在这项工作中，研究了由不可分离的晶胞组成的异质结构的拓扑优化。首先给出细胞形态，并在优化过程中保持不变。非局部数值均质化方法用于构造材料和结构尺度之间的介观本构关系。拓扑优化是在较高的介观尺度上对异质结构执行的，并且仅基于粗糙网格以节省计算量。数值研究表明，与使用分离假设的经典多尺度拓扑优化相比，结构刚度已得到显着改善。然而，