Abstract A combined topology optimization-graphic static approach is presented in this paper for manipulation and generation of equilibrium lightweight structures. Topology optimization is an effective tool for designing lightweight structures and truss-based designs. Graphic statics is also a powerful platform for truss-based designs and, more importantly, manipulation of such designs to satisfy pre-defined structural/load constraints. This work proposes coupling topology optimization and graphic statics in a sequential framework to take advantage of both methods in generating truss-based designs and offering a way to manipulate such structures without breaking the global equilibrium state and reducing truss forces. After post-processing and structural manipulation, results have shown structures with a uniform load distribution on all members. Optimized structures show an allowable load distribution manipulation and a significant reduction in member loads through form/force algorithms, presenting results with up to 4 and 100 times reduced maximum loads under the same state of global equilibrium. The work is essential in producing structures that avoid critical loads while having arbitrary load/boundary conditions that cannot be solved using existing methods.

中文翻译：

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使用图形静力学操作拓扑优化结构

摘要 本文提出了一种组合拓扑优化-图形静态方法，用于操作和生成平衡轻量级结构。拓扑优化是设计轻型结构和基于桁架的设计的有效工具。图形静力学也是基于桁架设计的强大平台，更重要的是，可以操纵此类设计以满足预定义的结构/载荷约束。这项工作提出了在顺序框架中耦合拓扑优化和图形静力学，以利用这两种方法来生成基于桁架的设计，并提供一种在不破坏全局平衡状态和减少桁架力的情况下操纵此类结构的方法。经过后处理和结构操作后，结果显示结构在所有构件上均具有均匀的载荷分布。优化的结构显示出允许的载荷分布操纵和通过形式/力算法显着减少的构件载荷，在相同的全局平衡状态下显示最大载荷降低多达 4 倍和 100 倍的结果。这项工作对于生产避免临界载荷同时具有使用现有方法无法解决的任意载荷/边界条件的结构至关重要。