Shakedown analysis is a powerful and efficient tool for calculating the safety factors of structures under variable and repeated external quasi-static loads, that can prevent structures from incremental and alternative plasticity collapses. RC slabs in practical engineering applications are usually under long-tern variable and cyclic loads, but their fatigue behavior was rarely reported in the literature, particularly for those governed by the Nielsen yield condition. In this paper, dual static and kinematic shakedown formulations based on displacement-finite elements and conic programming are developed. The resulting optimization problems, characterized by a huge number of variables, are effectively solved. A wide range of practical RC slabs with diverse geometries, loading and boundary conditions are investigated, precisely capturing the collapse modes in terms localized plastic dissipation energy and presenting moment distribution at fatigue state. Strengthening strategies are performed in regions with localized plastic dissipation energy, showing that the load-bearing capacity of such slabs increases significantly while incremental and alternative collapse modes are prevented.

中文翻译：

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循环荷载作用下 RC 板的承载力分析：双数值方法


安定分析是一种强大而有效的工具，用于计算结构在可变和重复的外部准静态载荷下的安全系数，从而防止结构发生增量和替代塑性坍塌。实际工程应用中的 RC 板通常承受长期可变和循环载荷，但它们的疲劳行为在文献中很少报道，特别是对于受 Nielsen 屈服条件支配的疲劳行为。在本文中，开发了基于位移有限元和圆锥规划的双静态和运动学稳定公式。由此产生的优化问题（以大量变量为特征）得到了有效解决。研究了具有不同几何形状、载荷和边界条件的各种实用 RC 板，根据局部塑性耗散能精确捕获塌陷模式，并呈现疲劳状态下的力矩分布。在具有局部塑性耗散能的区域进行加固策略，表明此类板的承载能力显着增加，同时防止了增量和交替坍塌模式。