结构反应的内蕴相关性与可靠度分析
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摘要
结构体系可靠度分析迄今是一个困难的问题。本文首先阐明了等价极值事件的概念,指出在对等价极值事件的概率积分过程中内蕴了不同事件之间的相关性信息。进而对这一概念进行推广,针对一般的复杂失效准则下的结构可靠度分析问题,构造相应的等价极值事件,从而将结构可靠度分析问题转化为极值分布的计算与积分问题。通过对结构静力可靠度与动力可靠度的实例分析表明,基于等价极值事件进行结构可靠度分析是可行的。
The structural system reliability evaluation is still a difficult problem.In the present paper,a typical case is studied to illustrate that an equivalent extreme value event could be constructed so that the correlation information is inherent in the probabilistic integration of the equivalent extreme value. This concept could then be extended to deal with the reliability evaluation of general structures with complex failure criterion through constructing an equivalent extreme value event to evaluate the reliability through a simple integration of the extreme value distribution.Numerical examples on static and dynamic reliability evaluation demonstrate that the proposed method is versatile and of acceptable accuracy.
The structural system reliability evaluation is still a difficult problem.In the present paper,a typical case is studied to illustrate that an equivalent extreme value event could be constructed so that the correlation information is inherent in the probabilistic integration of the equivalent extreme value. This concept could then be extended to deal with the reliability evaluation of general structures with complex failure criterion through constructing an equivalent extreme value event to evaluate the reliability through a simple integration of the extreme value distribution.Numerical examples on static and dynamic reliability evaluation demonstrate that the proposed method is versatile and of acceptable accuracy.
引文
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[15]WEN Y K.Method for random vibration of hysteret-ic systems[J].Journal of the Engineering Mechan-ics Division,1976,102(2):249-263.
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[17]艾晓秋.基于随机地震动模型的地下管线地震反应及抗震可靠度研究[D].同济大学,2005.(AI Xiao-qiu.Seismic Response and Reliability Evaluation ofUnderground Pipes Based on Stochastic Ground Mo-tion Model[D].Tongji University,2005.(in Chi-nese))
[2]WEN Y K.Reliability and performance-based design[J].Structural Safety,2001,23:407-428.
[3]SONG J H,Der Kiureghian A.Bounds on system re-liability by linear programming[J].Journal of Engi-neering Mechanics,2003,129(6):627-636.
[4]DITLEVSEN O.Narrow reliability bounds for struc-tural systems[J].Journal of Structural Mechanics,1979,107(4):453-472.
[5]CHEN K S,ZHANG S K,HUANG W.Artificialintelligence-βunzipping method in structural systemreliability analysis[J].Computers and Structures,1995,60(4):619-626.
[6]MAHADEVAN S,RAGHOTHAMACHAR P.A-daptive simulation for system reliability analysis oflarge structures[J].Computers and Structures,2000,77:725-734.
[7]YANG K,YOUNIS H.A semi-analytical MonteCarlo simulation method for system’s reliability withload sharing and damage accumulation[J].ReliabilityEngineering and System Safety,2005,87:191-200.
[8]李广慧,王东炜,傅方.小震下RC框架结构失效相关性研究[J].哈尔滨建筑大学学报,1999,32(2):7-10.(LI Guang-hui,WANG Dong-wei,FU Fang.A study on the failure correlation on the RC famestructure under small earthquakes[J].Journal ofHarbin University of C.E.&Architecture,1999,32(2):7-10.(in Chinese))
[9]朱位秋.随机振动[M].北京:科学出版社,1998.(ZHU Wei-qiu.Random Vibration[M].Beijing:Science Press,1998.(in Chinese)
[10]陈建兵,李杰.随机结构动力可靠度分析的极值概率密度方法[J].地震工程与工程振动,2004,24(6):39-44.(CHEN Jian-bing,LI Jie.The extreme valueprobability density function based method for dynam-ic reliability assessment of stochastic structures[J].Earthquake Engineering and Engineering Vibra-tion,2004,24(6):39-44.(in Chinese))
[11]李杰,陈建兵.随机结构非线性动力响应的概率密度演化方法[J].力学学报,2003,35(6):716-722.(LIJie,CHEN Jian-bing.The probability density evolu-tion method for analysis of dynamic nonlinear re-sponse of stochastic structures[J].Acta MechanicaSinica,2003,35(6):716-722.(in Chinese))
[12]CHEN J B,LI J.Extreme value distribution and reli-ability of nonlinear stochastic structures[J].Earth-quake Engineering and Engineering Vibration,2005,4(2):275-286.
[13]THOMAS J W.Numerical Partial DifferentialEquations[M].Springer-Verlag New York,Inc.,1995.
[14]李继华,等.建筑结构概率极限状态设计[M].北京:中国建筑工业出版社,1990.(LI Ji-hua.ProbabilisticLimit State Design of Building Structures[M].Bei-jing:China Architecture and Building Press,1990.(inChinese))
[15]WEN Y K.Method for random vibration of hysteret-ic systems[J].Journal of the Engineering Mechan-ics Division,1976,102(2):249-263.
[16]BABER T T,NOORI M N.Random vibration of de-grading,pinching systems[J].Journal of Engineer-ing Mechanics,1985,111(8):1010-1027.
[17]艾晓秋.基于随机地震动模型的地下管线地震反应及抗震可靠度研究[D].同济大学,2005.(AI Xiao-qiu.Seismic Response and Reliability Evaluation ofUnderground Pipes Based on Stochastic Ground Mo-tion Model[D].Tongji University,2005.(in Chi-nese))
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