Mechanical metastructures have been prevailing recently owing to their unusual mechanical responses. Despite notable progress in designing periodic metastructures, creating irregular and stochastic metastructures with optimized performance remains challenging because of the enlarged design space. In this study, we introduce a novel approach to realize the unstructured growth of irregular architectures for optimized metastructures. A “growth”-like design scheme is proposed to facilitate random yet controllable growth of predefined building blocks on an unstructured graph toward desired bulk properties. We also formulate a topology optimization framework that simultaneously optimizes building block selection and transformation (scaling, skew, and rotation) to generate metastructures with various optimized mechanical functionalities. These functionalities are achieved by harnessing the diverse homogenized material properties spanned by various frequency combinations of building blocks and the microstructure’s transformations. We discover metastructures that ensure geometric integrity and exhibit explicitly controllable and globally uniform feature sizes beneficial for fabrication. Moreover, the transformation-based topology optimization ensures these metastructures naturally conform to the boundaries of the design domain and can serve as mechanical infills. The proposed approach holds promise for uncovering optimized metastructures applicable across a wide array of engineering applications.

中文翻译：

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不规则架构的非结构化增长以优化元结构


机械元结构由于其不寻常的机械响应而最近盛行。尽管在设计周期性元结构方面取得了显着进展，但由于设计空间扩大，创建具有优化性能的不规则和随机元结构仍然具有挑战性。在这项研究中，我们引入了一种新颖的方法来实现不规则架构的非结构化增长，以优化元结构。提出了一种类似“增长”的设计方案，以促进非结构化图上预定义构建块的随机但可控的增长，以实现所需的整体属性。我们还制定了一个拓扑优化框架，可同时优化构建块选择和转换（缩放、倾斜和旋转），以生成具有各种优化机械功能的元结构。这些功能是通过利用不同的均质材料特性来实现的，这些材料特性由构建块的各种频率组合和微观结构的转变所跨越。我们发现元结构可以确保几何完整性，并表现出明确可控且全局统一的特征尺寸，有利于制造。此外，基于变换的拓扑优化确保这些元结构自然地符合设计域的边界，并且可以用作机械填充。所提出的方法有望揭示适用于各种工程应用的优化元结构。