随机钢结构的相关性与敏感性研究

Study on Correlation and Sensitivity of Stochastic Steel Structure

参数敏感性和失效相关性对于钢结构可靠度设计、优化和评定等具有重要的价值。本文以一简单函数为例来验证相关性和敏感性计算的正确性与高效性,紧接着以1个11-弦杆的桁架结构为例,重点研究了此种结构的参数敏感性和失效相关性,分析了变形能力极限状态下可靠度的重要性量度,将α、γ、δ和η作为4种重要性量度,分别研究了各随机变量对极限状态方程的敏感性和失效概率对随机变量均值和标准差的敏感性,并研究了基于变形能力的失效模式之间的相关性;将Polak-He和SQP算法引入到了桁架结构的可靠度与敏感性计算当中。主要得出如下结论:在此类桁架结构的可靠度计算中,节点坐标的变异性的影响不容忽略,有时甚至影响很大;4种重要性量度的变化趋势大体一致;SQP法和经过合适选取缩放系数的Polak-He法具有很高的验算点搜索效率。

Parametric sensitivity and failure correlations are important factors for reliability design,optimization and evaluation.To verify the validity and efficiency in correlation and sensitivity analysis,a simple limit-state function is selected as an example.Subsequently,an 11-bar truss is taken as a numerical example,and main attention is given to parametric sensitivity and failure correlation of this structure.Importance measures consisting of α,γ,δ and η are investigated under deformation capacity limit state.The sensitivity of limit state equation to each random variable and of failure probability to mean and standard deviation of random variables are researched,respectively.Furthermore,correlation between failure modes is also studied.The Polak-He and SQP algorithms are introduced to compute reliability and sensitivity.The main conclusions are as follows：the influence of variance of nodal coordinates on reliability of latticed truss can not be neglected,sometimes variance of nodal coordinates plays a predominant role in reliability analysis;changing laws of the four importance parameters are approximately consistent;SQP and Polak-He,if proper scaling factor is selected,have high efficiency to search for design point.