非平稳地震作用下强非线性结构动力可靠度分析  

Dynamic reliability analysis for strong nonlinear structures under non-stationary earthquake

作　　者：陈志强[1] 郑史雄[1] 张宁[1] 陈志伟[1] 李晰[1] CHEN Zhiqiang;ZHENG Shixiong;ZHANG Ning;CHEN Zhiwei;LI Xi(School of Civil Engineering,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]西南交通大学土木工程学院,成都610031

出　　处：《振动与冲击》2020年第19期121-129,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(U1434205,51508473)。

摘　　要：针对结构-地震动双重不确定影响下强非线性结构地震可靠度难以精确求解的问题,基于极值分布理论,提出了一种非平稳地震作用下非线性结构地震可靠度分析的高效数值方法。首先采用随机函数的降维思想对非平稳地震动进行降维模拟,将谱表达方法模拟非平稳地震动时需要的上千个高维随机变量减少到2个基本随机变量,大大减少了概率空间的维数;然后提出了一种改进的伪相关性折减拉丁超立方抽样方法确定积分点,从而对结构非线性地震响应极值分布分数矩进行有效估计,最后采用分数阶矩最大熵原理获得结构非线性地震响应极值分布,实现了小失效概率水平下非线性结构地震可靠度的精确估计。数值算例表明,该方法通过300次的动力分析就能够对结构-地震动双重不确定影响下强非线性结构地震响应的极值分布进行估计,其能够在兼顾效率和计算精度时对小失效概率水平下结构的动力可靠度进行精确计算,与既有方法相比,其计算量仅为现在方法的1/5,该方法能够为结构的地震风险评估提供一种有效途径。Aiming at the problem of a strong nonlinear structure’s seismic reliability being difficult to solve under influences of double-uncertainty of structure-earthquake,based on the extreme value distribution(EVD)theory,a highly efficient numerical method for seismic reliability analysis of strong non-linear structures under non-stationary earthquake was proposed.Firstly,the idea for dimension reduction of random function was used to do dimension reduction simulation,about one thousand high-dimension random variables needed for using the spectrum representation method to simulate a non-stationary earthquake were reduced to 2 elementary random variables to greatly reduce the dimension number of probability space.Then,an improved pseudo correlation reduction Latin hypercube sampling method was proposed to determine integration points,and effectively estimate fractional moments of structure nonlinear seismic response EVD.Finally,the maximum entropy principle for fraction moments was adopted to obtain structure nonlinear seismic response EVD,and realize the accurate estimation of seismic reliability of a non-linear structure under small failure probability level.Numerical example showed that the proposed method can estimate EVD of a strong nonlinear structure seismic response under influences of double-uncertainty of structure-earthquake through 300 hundred times of dynamic analysis;it can accurately calculate structure dynamic reliability under small failure probability level simultaneously considering efficiency and calculation accuracy;compared to the existing methods,its computation amount is only 1/5 of the existing method’s,the proposed method can provide an effective way for seismic risk evaluation of nonlinear structures.

关 键 词：非平稳 分数阶矩 极值分布 地震可靠性 双重不确定 

分 类 号：U452.28[建筑科学—桥梁与隧道工程]