计算结构首次穿越时间概率密度函数的新方法
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摘要
本文在M adsen等提出的积分方程方法基础上,采用单点FORM方法计算结构首次穿越问题中的条件穿越率、联合穿越率及首次穿越时间概率密度。提出的新方法计算简单,结果精确,适于进行脆性结构的首次穿越破坏分析。
Based on the integral equation method,which is presented by Madsen and so on,the conditional upcrossing rate,the joint upcrossing rate and the first-passage time probability density are obtained by use of single-point FORM method for first-passage of structures.The present method is suitable to analyze the first-passage failure of brittle structures due to its simple calculation and accurate result.
Based on the integral equation method,which is presented by Madsen and so on,the conditional upcrossing rate,the joint upcrossing rate and the first-passage time probability density are obtained by use of single-point FORM method for first-passage of structures.The present method is suitable to analyze the first-passage failure of brittle structures due to its simple calculation and accurate result.
引文
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[4]Zhu W Q,D engM L,Huang Z L.F irst-passage failure of quasi-integrab le ham ilton ian system s[J].J.Appl.M ech.,ASME,2002,69:274~282.
[5]Madsen P H,Krenk S.An integral equation m ethod for the first-passage prob lem in random vibration[J].J.Appl.M ech.,ASME,1984,51:674~679.
[6]Ch istein Hagen.Cond itional and joint failure surface crossing of stochastic processes[J].J.Eng.M ech.,ASCE,1992,118(9):1814~1839.
[7]朱位秋.随机振动[M].北京:科学出版社,1998.
[8]欧进萍.多自由度体系的动力可靠性分析[J].地震工程与工程振动,1987,7(4):51~61.
[2]Vanmarcke,E H.On the d istribution of the first passage tim e for normal stationary random processes[J].J.Appl.M ech.,ASME,1975,42:215~220.
[3]Naess A.C rossing rate statistics quadratic transformations of Gaussian processes[J].Prob.Engng.M ech.,2001,16:209~217.
[4]Zhu W Q,D engM L,Huang Z L.F irst-passage failure of quasi-integrab le ham ilton ian system s[J].J.Appl.M ech.,ASME,2002,69:274~282.
[5]Madsen P H,Krenk S.An integral equation m ethod for the first-passage prob lem in random vibration[J].J.Appl.M ech.,ASME,1984,51:674~679.
[6]Ch istein Hagen.Cond itional and joint failure surface crossing of stochastic processes[J].J.Eng.M ech.,ASCE,1992,118(9):1814~1839.
[7]朱位秋.随机振动[M].北京:科学出版社,1998.
[8]欧进萍.多自由度体系的动力可靠性分析[J].地震工程与工程振动,1987,7(4):51~61.
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