采用自适应Woodbury公式的框架结构高效动力分析与易损性计算方法

Efficient structural dynamic analysis and fragility solution methods for frame using adaptive Woodbury method

地震易损性分析是评价工程结构抗震安全性的重要手段,但在计算过程中通常需进行大量的动力时程分析,这导致其计算效率通常较低。该文旨在建立框架结构强震下的高效动力分析与倒塌易损性计算方法。使用纤维梁单元建立框架结构数值分析模型,引入隔离非线性理论进行局部材料弹塑性行为模拟,并通过对考虑P⁃Δ效应的几何刚度进行矩阵分解和摄动变换,提出了能够同时对局部材料弹塑性行为和几何非线性行为进行隔离表达的纤维梁模型控制方程,结合Woodbury公式进行控制方程求解,所提方法在结构动力非线性分析时能够避免整体刚度矩阵的反复更新,显著提升了求解效率;为克服动力Woodbury公式对时间步长选取的限制,进一步建立不同时间步长下该公式中相关系数矩阵的预处理机制和自适应调度机制,提出了基于自适应Woodbury公式的框架结构高效动力分析方法,在此基础上结合多条带法,建立了结构倒塌易损性曲线的快速计算方法。使用一个9层框架结构验证了所提方法的高效性和准确性。

Fragility analysis is of important in the evaluation of seismic safety of building structures under earthquake excitation.Such analysis usually involve a large number of dynamic time history analyses which indicate that the computational process is inef⁃ficient.This study focus on developing highly efficient dynamic nonlinearity analysis and collapse fragility analysis methods for frame structure.To this end,this study firstly use the fiber beam column element to establish the numerical model of the frame and use the inelasticity separated theory to model local material nonlinear behavior.The P-Δeffect is simulated by decomposing the cor⁃responding geometric stiffness and formulating the decomposed stiffness as perturbation expansion form.Thus,a novel governing equation of fiber beam column element that can uniformly depict the material nonlinear behavior and P-Δeffect using a separated way is developed and it can be solve by adopting the Woodbury formula directly.Because the proposed method can avoid the re⁃peatedly updating of global stiffness matrix in tradition method,the computational efficient is improved greatly.Then,to overcome the limitation of the dynamic Woodbury formula in the selection of time interval,a preconditioning mechanism and an adaptive scheduling mechanism for the coefficient matrices relating the implementation of Woodbury formula corresponding to various time intervals are established.Based on the above investigation,an adaptive Woodbury solution method for highly efficient dynamic non⁃linear analysis of frame structure is presented.Furthermore,by incorporating the multiple-stripe method,a fast collapse fragility analysis method of frame structure can be developed.Finally,the proposed method is verified by a nine-story frame structure.