Abstract This research bridges the gap between the numerical layout optimization method and the geometry-based analysis and design method of graphic statics. The study connects the two methods for the application of strut-and-tie models in reinforced concrete design. It suggests a new algorithm for the algebraic graphic statics of indeterminate trusses inspired by the layout optimization method. This research also contributes to the field of graphic statics by providing a formulation that generates form and force diagrams in a continuum, where the topology for none of the diagrams is initially provided. The generation of strut-and-tie models for reinforced concrete has extensively relied on optimization methods, which are helpful techniques for the initiation of a load path inside a continuous domain. However, the resulting truss model is a single answer, and there exists limited control to methodically modify the topology or the force distribution of the model. Furthermore, the minimized-weight truss does not guarantee a practical strut-and-tie model or an optimized performance of a reinforcement design. In contrast to the conventional optimization techniques with a single solution, the intuitive method of graphic statics provides the designer with a vast design space. It also offers explicit control over the geometry and force distribution of the generated truss models. The algorithm provided in this paper is applied to various continuous domains to systematically generate a variety of strut-and-tie models, their force diagrams, and constant stress fields. The production of the optimized truss model and its force distribution allows the direct interactive manipulations of the design while observing the changes in the stress fields and the reinforcement arrangement. The open-source repository of the implemented integrated algorithm and the examples used in this paper are also provided.

中文翻译：

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连续体中的图形静力学：钢筋混凝土的拉杆和拉杆模型

摘要 本研究弥补了数值布局优化方法与基于几何的图形静力学分析设计方法之间的差距。该研究将两种方法联系起来，以在钢筋混凝土设计中应用支柱和拉杆模型。它提出了一种受布局优化方法启发的不确定桁架代数图形静力学的新算法。这项研究还通过提供一个公式来生成连续体中的形状和力图，其中最初没有提供任何图的拓扑结构，从而为图形静力学领域做出贡献。钢筋混凝土的拉杆和拉杆模型的生成广泛依赖于优化方法，这是在连续域内启动载荷路径的有用技术。然而，由此产生的桁架模型是一个单一的答案，并且存在有限的控制来有条不紊地修改模型的拓扑或力分布。此外，最小重量的桁架并不能保证实用的支柱和拉杆模型或增强设计的优化性能。与传统的单一解决方案优化技术相比，图形静力学的直观方法为设计师提供了广阔的设计空间。它还提供对生成的桁架模型的几何形状和力分布的明确控制。本文提供的算法应用于各种连续域，以系统地生成各种支柱和拉杆模型、它们的力图和恒定应力场。优化的桁架模型及其受力分布的生成允许对设计进行直接交互操作，同时观察应力场和钢筋布置的变化。还提供了实现的集成算法的开源存储库和本文中使用的示例。