Abstract Topology optimization of trusses is one of the most inviting topics in the structural optimization field. In search for the computational efficiency, researchers have implemented many algorithms for this problem. With the advent of metaheuristic algorithms, structural optimization problems have become simpler to model; however, solution of these problems remains computationally expensive. The design candidates are generated by adding and removing the members heuristically and kinematically unstable candidates are mostly eliminated in metaheuristic truss topology optimization procedures. These procedures have a major flaw that needs to be overcome; metaheuristic algorithms may discard a promising but unstable design candidate although it can be repaired by adding and/or removing a few members. This study presents an algorithm to repair kinematically unstable planar truss design candidates. The algorithm first builds the connectivity matrix of the unstable candidates and identifies the structural components through geometric decomposition. Then, the repair takes place by adding and/or removing as less members as possible systematically in the conditions as absence of a basic truss and existence of unconnected or improperly connected components, supports, forces and/or remaining members. In addition, the presented algorithm gives information on how close is a candidate to a kinematically stable configuration.

中文翻译：

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基于几何分解的平面桁架拓扑运动稳定性修复算法

摘要 桁架的拓扑优化是结构优化领域最吸引人的课题之一。为了寻求计算效率，研究人员已经针对这个问题实现了许多算法。随着元启发式算法的出现，结构优化问题的建模变得更加简单；然而，解决这些问题的计算成本仍然很高。设计候选是通过启发式添加和删除成员生成的，并且在元启发式桁架拓扑优化程序中大多消除了运动学不稳定的候选。这些程序有一个需要克服的重大缺陷；元启发式算法可能会丢弃一个有前途但不稳定的设计候选，尽管它可以通过添加和/或删除一些成员来修复。本研究提出了一种修复运动学不稳定平面桁架设计候选的算法。该算法首先建立不稳定候选者的连通性矩阵，并通过几何分解识别结构成分。然后，在没有基本桁架和存在未连接或不正确连接的部件、支撑、力和/或剩余构件的情况下，通过系统地添加和/或移除尽可能少的构件来进行修复。此外，所提出的算法提供了有关候选者与运动稳定配置的接近程度的信息。在没有基本桁架和存在未连接或连接不当的组件、支撑、力和/或剩余构件的情况下，通过尽可能系统地添加和/或移除尽可能少的构件来进行修复。此外，所提出的算法提供了有关候选者与运动稳定配置的接近程度的信息。在没有基本桁架和存在未连接或连接不当的组件、支撑、力和/或剩余构件的情况下，通过尽可能系统地添加和/或移除尽可能少的构件来进行修复。此外，所提出的算法提供了有关候选者与运动稳定配置的接近程度的信息。