Strut-and-tie modelling (STM) is an effective and widely used method to design disturbed regions (D-regions) of reinforced concrete structures. Among the various steps of STM, finding a suitable truss-analogy model is the most challenging part. Even for experienced engineers it is difficult to find representative models for complex D-regions, and this task is even harder for three-dimensional (3D) D-regions. To date, only a few 3D STM models have been proposed by researchers for several complex D-regions, which leaves practitioners with little guidance. In order to solve this problem, a method is proposed to automatically generate 3D optimization-based STM (3D-OPT-STM) models. The generation method comprises a compliance-based topology optimization process that generates optimized structural forms by maximizing stiffness, a topology extraction method, and a shape optimization method. In this study, three 3D-OPT-STM models are generated for typical 3D D-regions, and their performances are compared to manually created STM models. The generated 3D-OPT-STM models result in more economical designs. Moreover, geometrical and loading parameter studies demonstrate the applicability and robustness of the proposed method.

中文翻译：

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基于优化的钢筋混凝土三维支撑模型

杆系模型（STM）是一种有效且广泛使用的方法，用于设计钢筋混凝土结构的扰动区域（D区域）。在STM的各个步骤中，找到合适的桁架模拟模型是最具挑战性的部分。即使对于有经验的工程师，也很难找到适用于复杂D区域的代表性模型，而对于三维（3D）D区域，此任务甚至更加困难。迄今为止，研究人员仅针对几个复杂的D区域提出了一些3D STM模型，这给从业人员提供了很少的指导。为了解决这个问题，提出了一种自动生成基于3D优化的STM（3D-OPT-STM）模型的方法。生成方法包括基于合规性的拓扑优化过程，该过程通过最大化刚度来生成优化的结构形式，拓扑提取方法和形状优化方法。在这项研究中，针对典型的3D D区域生成了三个3D-OPT-STM模型，并将其性能与手动创建的STM模型进行了比较。生成的3D-OPT-STM模型可实现更经济的设计。此外，几何和载荷参数研究证明了该方法的适用性和鲁棒性。