非Gauss随机特性下的结构首次失效时间研究  

Structural First Failure Times Under Non-Gaussian Stochastic Behavior

作　　者：何军[1] 

机构地区：[1]上海交通大学船建学院土木工程系,上海200240

出　　处：《应用数学和力学》2007年第11期1325-1332,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(50478017)

摘　　要：提出了一个基于结构响应矩的解析方法,用来计算具有非Gauss特性结构的首次失效时间.在该方法中,首先采用其系数可通过结构反应矩(偏态系数和峰度系数等)计算的幂级数,将非Gauss结构反应变换为标准Gauss过程.然后,利用变换的标准Gauss过程计算原结构反应过程关于某临界界限的平均超越率、平均群超尺度和初始超越概率.最后,在修正超越率为独立的假定下,建立了首次超越时间的计算公式.Gauss过程激励下非线性单自由度振动系统的分析,不仅说明了该方法的应用过程,也通过与Monte Carlo模拟和传统Gauss模型方法的对比分析,证明了该方法的精确性和效率.An analytical moment-based method for calculating structural first failure times under non Gaussian stochastic behaviour is proposed. In the method, a power series that is constant can be obtained from response moments （skewness, kurtosis, etc. ） was used firstyl to map a non-Gaussian structuralresponse into a standard Gaussian process, then mean up-crossing rates, mean clmnp size and the initial passage probability of a critical barrier level by the original structural response were estimated. Finally, the formula for calculating first failure times was established on the aasumption that corrected up-crossing rates are independent. An analysis of a nonlinear single-degree-of-freedom dynamical system excited by a Gaussian model of load not only demonstrates the usage of the proposed method but also shows the accuracy and efficiency of the proposed method by comparisons between the present method and other methods such as Monte Carlo simulation and the traditional Gaussina model.

关 键 词：首次失效时间 非Gauss结构特性 超越率 幂级数 

分 类 号：O29[理学—应用数学]