基于隔离非线性理论的结构地震损伤高效分析方法

EFFICIENT SEISMIC DAMAGE ANALYSIS METHOD OF STRUCTURES UPON THE INELASTICITY-SEPARATED THEORY

  • 摘要: 基于韧性的地震工程已成为建筑抗震领域的重要发展方向,在进行建筑抗震韧性评估时,对结构在地震作用下的损伤状态进行精准刻画是评估建筑功能损失及可恢复性的基础。现有研究多采用层间位移角、构件杆端转角等唯象的宏观工程需求参数评估结构或构件损伤,然而,对于复杂结构,此类指标不仅难以用来对结构损伤状态进行精细化描述,导致评估结果存在较大的不确定性,也缺乏明确的物理意义,此外,评估结构地震损伤需以非线性动力分析数据为基础,而传统方法在进行此类分析时需实时更新和分解大规模结构切向刚度矩阵,导致计算效率低。针对上述问题,该文基于隔离非线性理论提出了一种高效的结构精细化地震损伤分析方法,该方法首先将非线性材料的应变分解为线弹性、损伤和塑性三部分,并在单元内构造损伤和塑性应变场模型;随后结合虚功原理建立隔离损伤-塑性控制方程,并引入Woodbury公式进行求解,使结构动力非线性分析的主要计算量集中于小规模损伤和塑性矩阵的更新和分解,避免了大规模整体切线刚度矩阵耗时的迭代更新,显著提升计算效率;最后,基于分解出的损伤和塑性应变建立了结构中任意部位的损伤量化计算方法,由于本文方法中引入的损伤和塑性应变不仅具有明确的物理意义,且可在每个增量步的控制方程求解过程中实时获取,因而不仅能够对结构损伤状态进行精准刻画,也可用来对结构在地震作用下的损伤分布及其演化过程进行精细化描述和追踪。

     

    Abstract: Resilience-based earthquake engineering methodology plays an important role in the field of structural aseismic design. Within a framework to assess the aseismic resilience of buildings, accurately determining damage states for individual buildings under earthquake excitations is basic to predict buildings’ functionality loss and recoverability. Existing studies determined a damage state for each component with phenomenological engineering demand parameters (EDPs) such as the storey drift ratio, the nodal rotation at the beam end, etc., from the nonlinear dynamic processes data. Nevertheless, phenomenological EDPs may not suffice to predict refined structural damage in irregular complex structures, which leads to the resilience assessment results arising a large uncertainty, and phenomenological EDPs are lack of clear physical meanings. In addition, the nonlinear dynamic analysis based on the classical finite element method (FEM) requires the large-scale tangent stiffness matrix that needs to be updated and decomposed iteratively in real time to calculate structural damage, which reduces the calculation efficiency exceedingly. Aiming to solve the problems mentioned above, an efficient seismic damage analysis method of structures is proposed upon the inelasticity-separated theory. First the novel method proposed decomposes the total strain of a nonlinear material into three parts, elastic strain, damage strain and plastic strain, and defines the damage and plastic strain distribution fields within elements. Further a novel governing equation with the feature that is capable of realizing the elasticity, damage and plasticity separation is established by the grounds of the principle of virtual work, and the proposed governing equation is solved via the efficient mathematical Woodbury formula. Consequently, the computational effort of the nonlinear structural dynamic analysis only focuses on the updating and factorization of the damage and plastic matrices with small-rank, and during the iteration process the updating and factorization of tangent stiffness matrix in the classical FEM are avoided, which significantly improves the efficiency of nonlinear calculation. Finally, a local damage quantification approach for structures is established by the basis of the decomposed damage and plastic strains. Because the plastic and damage strains, introduced by the governing equation proposed and obtained in real time during the iteration process, have definite physical meanings, the refined structural damage distribution and evolution can be depicted accurately.

     

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