基于Legendre正交多项式逼近法的结构可靠性分析  

STRUCTURAL RELIABILITY ANALYSIS USING LEGENDRE ORTHOGONAL POLYNOMIAL APPROXIMATE METHOD

作　　者：宫凤强[1] 李夕兵[1] 

机构地区：[1]中南大学资源与安全工程学院

出　　处：《工程力学》2008年第6期225-229,共5页Engineering Mechanics

基　　金：国家自然科学基金重大项目(50490274);国家“973”资助项目(2002CB412703)

摘　　要：提出了结构可靠性分析的Legendre正交多项式逼近法。主要是基于数值逼近原理,以Legendre正交函数族做基,利用功能函数的高阶矩信息,通过计算功能函数概率密度函数的逼近表达式,然后根据工程结构可靠性的一般表达式来计算结构的失效概率,进行可靠性分析。通过数值检验,证明该方法可以很好地逼近各种经典理论分布曲线(正态分布、指数分布等6种经典分布)。文后给出了结构构件失效概率的实例计算,并和其它几种常用方法进行对比,进一步表明了Legendre正交多项式数值逼近法在结构可靠性分析理论上的正确性和实用性。A method to estimate the failure probability of structures using Legendre orthogonal polynomial approximate method （LPAM） was presented. Based on the numerical approximate theory, the Legendre orthogonal polynomial with higher moments of performance function was used to approximate the probability density function of performance function. The failure probability of structures can be obtained according as computing ecumenical expression of structure reliability analysis. Six most commonly-used theoretical distributions including normal, lognormal, extreme value I, Gama, exponential and Weibull distributions, were used to verify the approximate characteristic of LPAM. A structure component example was given for illustrative purposes. The result shows that the failure probability of structures using LPAM is agreed well with those obtained by the conventional reliability methods.

关 键 词：结构可靠性 Legendre正交多项式 概率密度函数 失效概率 数值逼近 

分 类 号：TU311.2[建筑科学—结构工程] O159[理学—数学]