摘要
为了解决工程实际中高维非线性或功能函数为隐式的情况给结构数值分析带来的困难,文中提出了一种新型结构可靠性直接分析方法.首先利用降维算法将维函数展开为个一维函数的形式,再将各一维函数中的变量运用变量转换方法进行变换,并结合Gauss-Hermite数值积分方法,计算得到个一维函数的原点矩及中心矩,将所得矩信息与Taylor展开计算出的结构功能函数的中心矩结合,再借助Edgeworth级数法推导出结构功能函数的累积分布函数表达式,并运用结构可靠性理论计算得到结构功能函数的失效概率.该方法在计算过程中无需进行多重积分计算功能函数的统计矩.数值算例结果表明该方法正确可行.
In order to overcome the difficulties in structural numerical analysis caused by the high-dimension nonlinearity or the implicit performance functions in engineering practice,a numerical method to directly analyze the structural reliability is proposed. In this method,the n-dimension function is changed into n single-dimension functions via the dimension reduction,and the origin moment and the central moment of each single-dimension function are calculated through the variable transformation of the single-dimension functions and the Gauss-Hermite numerical integration. Then,the moment information is combined with the central moment of the structural performance function obtained by Taylor expansion,the cumulative distribution function of the structural performance function is deduced with the help of Edgeworth series,and the failure probability of the structural performance function is calculated based on the structural reliability theory. The proposed method avoids the multiple integrations for the statistical moment calculation of the performance function. Numerical examples show that this method is correct and feasible.
出处
《华南理工大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2016年第4期130-134,142,共6页
Journal of South China University of Technology(Natural Science Edition)
基金
吉林省科技厅基金资助项目(201205001
201215048)
国家重大科学仪器设备开发专项(2012YQ030075)~~
作者简介
孟广伟（1959-）,男,博士,教授,主要从事疲劳与断裂研究.E-mail：mgw@jlu.edu.cn
通信作者：李锋（1977-）,男,博士,副教授,主要从事疲劳与断裂研究.E-mail：fengli@jlu.edu.cn
