Abstract In this paper, a novel numerical procedure is proposed for the force-displacement description of out-of-plane collapse in masonry structures. The numerical procedure herein proposed represents one first attempt to couple limit analysis-based solutions to displacement-based evolutive analysis strategies. Limit-analysis based solutions are considered trustworthy to investigate collapse mechanisms in masonry structures, even though they cannot be used in displacement-based seismic assessment procedures (e.g. pushover analysis), while displacement-based evolutive analysis strategies (e.g. block-based and anisotropic continuum approaches), which can undertake this last task, are typically computationally demanding and their mechanical characterization is often very challenging. In this research, a genetic algorithm NURBS-based adaptive homogenized upper bound limit analysis is firstly adopted to compute the collapse mechanism that the structure (of any geometrical complexity) experiences for a given loading condition. Then, the 3D geometry of the collapse mechanism is imported in incremental-iterative step-by-step evolutive analysis frameworks to perform pushover analysis. In particular, two numerical modelling approaches are conceived to this aim, both lumping all the mechanical nonlinearities into tight zones located in correspondence of the cracks defined in the collapse mechanism previously computed. The first one uses 3D plastic damaging strips governed by a standard nonlinear continuum constitutive law. The second approach adopts non-standard zero-thickness contact-based interfaces governed by a cohesive-frictional contact behaviour previously developed by the authors for the brick-to-brick mechanical interaction. A number of meaningful structural examples show the effectiveness of the numerical procedure proposed. Pushover curves obtained through different modelling strategies are also critically compared.

中文翻译：

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砌体结构中平面外倒塌机制的力-位移描述的数值程序

摘要 在本文中，提出了一种新的数值方法来描述砌体结构中平面外倒塌的力-位移。此处提出的数值程序代表了将基于极限分析的解决方案与基于位移的演化分析策略相结合的第一次尝试。尽管基于极限分析的解决方案不能用于基于位移的地震评估程序（例如推覆分析），但基于位移的演化分析策略（例如基于块和各向异性连续体）方法），可以承担最后一项任务，通常对计算要求很高，并且它们的机械特性通常非常具有挑战性。在这项研究中，首先采用基于遗传算法 NURBS 的自适应均质化上限分析来计算结构（具有任何几何复杂性）在给定加载条件下所经历的坍塌机制。然后，将倒塌机构的 3D 几何形状导入到增量迭代逐步演化分析框架中，以执行 Pushover 分析。特别是，为了这个目的，设想了两种数值建模方法，两者都将所有机械非线性集中到与先前计算的坍塌机制中定义的裂缝对应的紧密区域中。第一个使用由标准非线性连续体本构律控制的 3D 塑料损坏条。第二种方法采用非标准的基于零厚度接触的界面，由作者先前为砖对砖机械相互作用开发的内聚摩擦接触行为控制。许多有意义的结构示例显示了所提出的数值程序的有效性。通过不同的建模策略获得的 Pushover 曲线也进行了严格的比较。