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A variational-based non-smooth contact dynamics approach for the seismic analysis of historical masonry structures
Computer Methods in Applied Mechanics and Engineering ( IF 6.9 ) Pub Date : 2024-09-03 , DOI: 10.1016/j.cma.2024.117346
Nicola A. Nodargi , Paolo Bisegna

A variational formulation of the non-smooth contact dynamics method is proposed to address the dynamic response of historical masonry structures modeled as systems of 3D rigid blocks and subjected to ground excitation. Upon assuming a unilateral-frictional contact law between the blocks, the equations of motions are formulated in a time-discrete impulse theorem format in the unknown block velocities and contact impulses. The variational structure of the problem to be solved at each time step is proven. On that basis, the numerical method requires at each time step to perform a collision detection that identifies antagonist contact points based on the given structural configuration, to solve a second-order conic programming problem that outputs block velocities and contact impulses, and to update the structural configuration for the solution to advance in time. As a merit of the formulation, large-scale problems can be robustly and efficiently addressed thanks to the convex setting of the time-step optimization problem. Numerical results are presented to test the computational performances of the proposed approach. Benchmark problems provide numerical evidence that the formulation is consistent with event-driven solutions based on the classical Housner impact model. The dynamic response, failure domains, and fragility functions of real-size masonry structures are then explored under ground impulse or earthquake excitation. The obtained results prove the reliability of the present computational method for the dynamic analysis and seismic assessment of historical masonry constructions of engineering interest.

中文翻译:


一种基于变分的非光滑接触动力学方法,用于历史砌体结构的地震分析



提出了非光滑接触动力学方法的变分公式,以解决历史砌体结构的动力学响应问题,该结构被建模为 3D 刚性块系统并受到地面激励。在假设块之间存在单侧摩擦接触定律后,运动方程以未知块速度和接触冲量的时间离散冲量定理格式表示。证明了每个时间步长要解决的问题的变分结构。在此基础上,数值方法要求在每个时间步长执行碰撞检测,根据给定的结构配置识别拮抗剂接触点,求解输出块速度和接触脉冲的二阶圆锥规划问题,并更新解决方案的结构配置以及时推进。作为该公式的一个优点,由于时间步长优化问题的凸设置,可以稳健且有效地解决大规模问题。给出了数值结果,以测试所提方法的计算性能。基准问题提供了数值证据,证明该公式与基于经典 Housner 影响模型的事件驱动解决方案一致。然后,在地面冲击或地震激励下探索了真实大小的砌体结构的动力响应、破坏域和脆性函数。所得结果证明了该计算方法对工程意义的历史砌体结构的动力分析和抗震评估的可靠性。
更新日期:2024-09-03
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