Homogenization theory forms the basis for solving the topology optimization problem (TOP) formulated for designing composite materials. Homogenization is proved to be an efficient approach to effectively determine the equivalent macroscopic properties of the composite material. It relies on the assumption that the composite material presents a periodic pattern on a microstructural level; the simplest repeating unit of the microstructure, that if isolated represents exactly the macroscopic behaviour of the material, is called the \(unit\ cell\). Scope of homogenization is to determine the macroscopic (or else effective) properties of the non-homogeneous unit cell, that is, determine the properties of the unit cell as if it was composed by homogeneous material. In this study, a simple methodology is proposed where homogenization is implemented on a 3D lattice unit cell, with its radius being considered as the alternating parameter for the homogenization procedure; different values of the radius result to different unit cell configurations and hence, to different equivalent properties. A fitting process takes place in order to appropriately model the variations of the obtained effective properties w.r.t the design parameter. The corresponding, homogenization-based TOP is formed and the accuracy of the proposed methodology is assessed on several case studies.

均质化理论构成了解决设计复合材料的拓扑优化问题（TOP）的基础。均质被证明是有效确定复合材料等效宏观性能的有效方法。它基于这样的假设，即复合材料在微观结构水平上呈现出周期性的模式。微观结构中最简单的重复单元，如果被孤立地恰好代表了材料的宏观行为，则被称为\（unit \ cell \）。均质化的范围是确定非均质晶胞的宏观（或有效）特性，即确定该晶胞的性质，就好像它是由均质材料组成的一样。在这项研究中，提出了一种简单的方法，在3D晶格单元上进行均质化，其半径被视为均质过程的替代参数。半径的不同值会导致不同的晶胞配置，从而导致不同的等效属性。进行拟合过程以适当地建模所获得的有效特性w的变化。[R 。Ť设计参数。形成了相应的基于均质化的TOP，并在一些案例研究中评估了所提出方法的准确性。