This paper introduces a new concurrent topology optimization approach based on adaptive geometric components for designing and fabricating cellular composites using 3D printing. The key idea behind this approach is to model adaptive geometric components by projecting them onto macro- and microelement density fields, combining them to calculate the effective densities of grid elements. The cellular structure at the macro- and microstructural levels are optimized at the same time by finding optimal geometric parameters for adaptive geometric components. The proposed method enables designing high-porosity composites on a coarse finite element mesh without material homogenization. As a result, it provides a cost-effective way to obtain optimal designs of cellular composites and simultaneously control the length scales of both the macro- and microstructures. The effectiveness of this method is demonstrated through several numerical examples. This work also explores the ability to realize concurrent optimized structures using additive manufacturing.

中文翻译：

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用于增材制造的蜂窝复合材料的自适应并发拓扑优化

本文介绍了一种新的基于自适应几何组件的并发拓扑优化方法，用于使用 3D 打印设计和制造蜂窝复合材料。这种方法背后的关键思想是通过将自适应几何组件投影到宏观和微观元素密度场上，将它们组合起来计算网格元素的有效密度来对它们进行建模。通过寻找自适应几何组件的最佳几何参数，同时优化宏观和微观结构级别的细胞结构。所提出的方法能够在没有材料均质化的情况下在粗略的有限元网格上设计高孔隙率复合材料。因此，它提供了一种经济高效的方法来获得蜂窝复合材料的最佳设计，并同时控制宏观和微观结构的长度尺度。通过几个数值例子证明了该方法的有效性。这项工作还探索了使用增材制造实现并行优化结构的能力。