This paper proposes a clustering-based concurrent topology optimization method for designing additive manufacturable cellular structures. In the context of multiscale topology optimization, the macrodesign domain can be divided into several subdomains (components) to reduce the number of microstructures which are needed to be optimized. However, in previous works, the division pattern is either artificially decided and fixed during the iteration process or updated according to a fixed parameter range. In this paper, a dynamic clustering strategy is developed to automatically divide the macrodesign domain into several subdomains according to the directions and ratio of the principal stress. K-means algorithm is adopted here for clustering; the advantages are that no predefined range is needed to group the microstructures and the number of microstructures used in the optimization can be arbitrarily specified. The macrostructure and the representative microstructures are optimized simultaneously using a density-based method. Each iteration consists of three sequential steps: First, the macrovariables are updated one step forward. Then, get the stress tensors from the macrovariables updating step and perform the clustering analysis. In the end, update the microvariables one step forward under the current clustering pattern and start the next iteration until the optimization converges. Several numerical examples are presented to demonstrate the effectiveness of the proposed method.

提出了一种基于聚类的并发拓扑优化方法，用于设计可制造的加性蜂窝结构。在多尺度拓扑优化的上下文中，可以将宏设计域划分为几个子域（组件），以减少需要优化的微观结构的数量。但是，在以前的工作中，分割模式是在迭代过程中人为确定和固定的，或者是根据固定的参数范围进行更新的。本文提出了一种动态聚类策略，可以根据主应力的方向和比例将宏设计域自动划分为几个子域。ķ-均值算法在这里采用聚类；优点是不需要预定义的范围来组织微结构，并且可以任意指定优化中使用的微结构的数量。使用基于密度的方法同时优化宏观结构和代表性的微观结构。每次迭代包括三个连续步骤：首先，将宏变量向前更新一个步骤。然后，从宏变量更新步骤中获取应力张量并执行聚类分析。最后，在当前的聚类模式下向前更新微变量，并开始下一次迭代，直到优化收敛为止。几个数值例子被提出来证明所提方法的有效性。