Nonlinear seismic analysis, an approach to evaluate the seismic performance of a structure, is facing the challenge of computational efficiency for large-scale and high-fidelity simulation. This paper proposes an adaptive model order reduction (MOR) method based on the damage evolution among the overall structure to alleviate the computational burden. The damage state of each component during seismic loadings is distinguished as the initial-elastic phase, the plastic-damage phase, and the residual-elastic phase. In order to exploit the potential of model order reduction based on the damage evolution, a duration spectrum analysis is utilized to evaluate the characteristics of the residual-elastic phase for SDOF systems with bilinear hysteretic behaviour. Thus, an adaptive MOR method has been proposed to handle the nonlinear dynamic analysis of structures during different damage evolution phases. The overall structure is adaptively partitioned into linear substructures and nonlinear substructures on the basis of the time-varying damage distribution. The model order of linear substructures is reduced using the initial stiffness-based vibration modes, while nonlinear substructures that keep in the residual-elastic phase are reduced using the tangent-stiffness-based vibration modes. The residual displacements of nonlinear substructures are treated as the initial deformation during the residual-elastic phase. Compared with the traditional time step integration method, the proposed adaptive MOR method is able to increase the computational efficiency as yielding comparative results.

中文翻译：

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基于损伤演化的自适应模型降阶方法在非线性地震分析中的应用

非线性地震分析是一种评估结构抗震性能的方法，目前正面临着大规模和高保真模拟的计算效率挑战。提出了一种基于整体结构之间的损伤演化的自适应模型降阶（MOR）方法，以减轻计算量。在地震荷载作用下，每个组件的破坏状态可分为初始弹性阶段，塑性破坏阶段和残余弹性阶段。为了利用基于损伤演化的模型降阶的潜力，使用持续时间谱分析来评估具有双线性滞后行为的SDOF系统的残余弹性相的特征。从而，提出了一种自适应的MOR方法来处理结构在不同损伤演化阶段的非线性动力学分析。根据随时间变化的损伤分布，将整个结构自适应地分为线性子结构和非线性子结构。使用基于刚度的初始振动模式可以减少线性子结构的模型顺序，而使用基于切线刚度的振动模式可以减少保持在残余弹性相中的非线性子结构的模型顺序。非线性子结构的残余位移被视为残余弹性阶段的初始变形。与传统的时间步长积分方法相比，提出的自适应MOR方法能够提高计算效率，产生比较结果。