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Mixed Lagrangian formalism for dynamic analysis of self-centering systems

机译：自定心系统动态分析混合拉格朗日形式主义

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摘要

This paper presents two models for the analysis of self-centering concentrically braced frames (SC-CBFs) with multiple rocking sections. Both models are developed within the mixed Lagrangian formalism (MLF). For these models, MLF leads to a quadratic optimization problem at each time step where the internal forces at the end of the time step are the design variables. The first model is more general and explicitly models the truss elements. The second model is simplified and utilizes a macromodel. This model is easier to implement for initial designs, optimization, and parametric studies. For the purpose of formulating the simplified model, a new rotational contact element is developed and added to the MLF to describe the behavior of the rocking sections. Both models are compared to results obtained using the finite-element method. Although the comparison shows a good agreement, MLF is shown to allow much larger time increments for convergence. This considerably reduces the computational effort and central processing unit time. The simplified model is extended for three-dimensional analysis of SC-CBFs. This shows that the proposed models can be easily extended using relatively simple transformation matrices.
机译：本文呈现了两种模型，用于分析具有多个摇摆部分的自定心同心支撑框架（SC-CBF）。两种型号都在混合拉格朗日形式主义（MLF）内开发。对于这些模型，MLF在每次步骤中导致二次优化问题，其中内部力在时间步长的内部力是设计变量。第一个模型更通用，并明确地模拟桁架元素。简化了第二种模型并利用了Macromodel。此模型更容易实现初始设计，优化和参数研究。为了制定简化模型，开发了一种新的旋转接触元件并将其添加到MLF中以描述摇摆部分的行为。将两种模型与使用有限元方法获得的结果进行比较。虽然比较显示了良好的一致性，但MLF被证明允许收敛的更大的时间增量。这大大降低了计算工作和中央处理单元时间。简化模型延长了SC-CBFS的三维分析。这表明所提出的模型可以使用相对简单的变换矩阵轻松扩展。

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