非平稳地震作用下随机结构动力可靠度计算
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摘要
对非平稳地震作用下的含随机参数结构,建议了一类结构体系动力可靠度的数值模拟求解方法。把结构动力方程写成状态方程形式,采用精细积分法对状态方程进行数值求解,将结构响应表达为一系列随机系数和离散时刻处随机激励乘积的和形式。随机系数为结构随机参数的函数,反映结构随机参数对随机响应的影响。在确定性结构非平稳随机响应时域分析方法的基础上,采用不含交叉项的二次多项式对该随机系数进行重构,获得了结构响应关于结构随机参数和离散时刻处随机激励的显式表达式。基于该显式表达式,利用数值模拟技术可以方便地进行首次超越失效准则下结构体系动力可靠度的求解。对一榀非平稳地震作用下的含随机参数框架进行了结构体系动力可靠度分析,并在计算精度和计算效率上与传统蒙特卡罗法进行了比较,结果显示所提出的方法具有理想的精度和相当高的效率。
A numerical simulation method is proposed in this paper for system dynamic reliability analysis of stochastic structures under non-stationary seismic excitations.Structural dynamic equations are first transformed into the form of state equations and then solved by the precise time integral method,which yields the structural responses as the combination of a series of products of random coefficients and random excitations at each discrete instant.The random coefficients are the functions of structural random parameters,reflecting the influence of the structural random parameters on the random responses.Based on the time-domain method for analysis of non-stationary random responses of deterministic structures,the random coefficients are fitted as quadratic functions of the structural random parameters without cross-terms,which leads to the explicit expressions of structural responses with regard to the structural random parameters and random excitations at each instant.By using the explicit expressions deduced,numerical simulation techniques can be readily employed to analyze the structural system dynamic reliability beyond the first excursion failure criterion.The system dynamic reliability of a stochastic frame structure subjected to non-stationary seismic excitation is obtained by the proposed method and the traditional Monte-Carlo method.The calculation accuracy and efficiency of the proposed method are compared with those of the Monte-Carlo method,showing that the present approach has ideal accuracy and considerably high efficiency.
A numerical simulation method is proposed in this paper for system dynamic reliability analysis of stochastic structures under non-stationary seismic excitations.Structural dynamic equations are first transformed into the form of state equations and then solved by the precise time integral method,which yields the structural responses as the combination of a series of products of random coefficients and random excitations at each discrete instant.The random coefficients are the functions of structural random parameters,reflecting the influence of the structural random parameters on the random responses.Based on the time-domain method for analysis of non-stationary random responses of deterministic structures,the random coefficients are fitted as quadratic functions of the structural random parameters without cross-terms,which leads to the explicit expressions of structural responses with regard to the structural random parameters and random excitations at each instant.By using the explicit expressions deduced,numerical simulation techniques can be readily employed to analyze the structural system dynamic reliability beyond the first excursion failure criterion.The system dynamic reliability of a stochastic frame structure subjected to non-stationary seismic excitation is obtained by the proposed method and the traditional Monte-Carlo method.The calculation accuracy and efficiency of the proposed method are compared with those of the Monte-Carlo method,showing that the present approach has ideal accuracy and considerably high efficiency.
引文
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[16]乔红威,吕震宙.非平稳随机激励下随机结构的动力可靠性分析[J].固体力学学报,2008,29(1):36—40.
[17]乔红威,吕震宙,关爱锐,等.平稳随机激励下随机结构动力可靠度分析的多项式逼近法[J].工程力学,2009,26(2):60—64.
[18]Brenner C E,Bucher C.A contribution to the SFE-based reliability assessment of nonlinear structuresunder dynamic loading[J].Probabilistic EngineeringMechanics,1995,10(4):265—273.
[19]陈颖,王东升,朱长春.随机结构在随机载荷下的动力可靠度分析[J].工程力学,2006,23(10):82—85.
[20]李杰,陈建兵.随机结构动力可靠度分析的概率密度演化方法[J].振动工程学报,2004,17(2):121—125.
[21]陈建兵,李杰.复合随机振动系统的动力可靠度分析[J].工程力学,2005,22(3):52—57.
[22]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131—136.
[23]Bucher C G,Bourgund U.A fast and efficient re-sponse surface approach for structural reliability prob-lems[J].Structural Safety,1990,7(1):57—66.
[24]Cressie N.Statistics for Spatial Data[M].NewYork:John Wiley,1993.
[25]Kanai K.Semi-empirical formula for the seismic char-acteristics of the ground motion[J].Bulletin of theEarthquake Research Institute,University of Tokyo,1957,35(2):308—325.
[26]孙广俊,李鸿晶.平稳随机地震地面运动过程模型及其统计特征[J].地震工程与工程振动,2004,24(6):21—26.
[2]Lin Y K,Cai G Q.Probability Structural Dynamics:Advanced Theory and Application[M].New York:McGraw Hill College Div.,1995.
[3]Kleiber M,Hien T D.The Stochastic Finite ElementMethod:Basic Perturbation Technique and ComputerImplementation[M].Chichester:Wiley,1992.
[4]Kaminski M.Generalized stochastic perturbationtechnique in engineering computations[J].Mathemat-ical and Computer Modeling,2010,51:272—285.
[5]林家浩,易平.线性随机结构的平稳随机响应[J].计算力学学报,2001,18(4):402—408.
[6]Spanos P D,Ghanem R G.Stochastic finite elementexpansion for random media[J].Journal of Engineer-ing Mechanics Division,1989,115(5):1 035—1 053.
[7]李杰.复合随机振动分析的扩阶系统方法[J].力学学报,1996,28(1):66—75.
[8]李杰,陈建兵.随机结构动力反应的概率密度演化方法[J].力学学报,2003,35(4):437—442.
[9]李杰,陈建兵.随机结构复合随机振动分析的概率密度演化方法[J].工程力学,2004,21(3):90—95.
[10]Chen J J,Che J W,Sun H A,et al.Probabilistic dy-namic analysis of truss structures[J].Structural En-gineering and Mechanics,2002,13(2):233—239.
[11]高伟,陈建军,马娟,等.平稳随机激励下线性随机桁架结构动力响应分析[J].振动工程学报,2004,17(1):44—48.
[12]曹宏,李秋胜,李芝艳.随机结构动力反应和可靠性分析[J].应用数学和力学,1993,14(10):931—938.
[13]胡太彬,陈建军,高伟,等.平稳随机激励下随机桁架结构动力可靠性分析[J].力学学报,2004,36(2):241—246.
[14]Spencer B F Jr,Elishakoff I.Reliability of uncertainlinear and nonlinear systems[J].Journal of Engineer-ing Mechanics,1988,114(1):135—149.
[15]Papadimitriou C,Beck J L,Katafydiotis L S.Asymp-totic expansions for reliability and moments of uncer-tain systems[J].Journal of Engineering Mechanics,1997,123(12):1 219—1 229.
[16]乔红威,吕震宙.非平稳随机激励下随机结构的动力可靠性分析[J].固体力学学报,2008,29(1):36—40.
[17]乔红威,吕震宙,关爱锐,等.平稳随机激励下随机结构动力可靠度分析的多项式逼近法[J].工程力学,2009,26(2):60—64.
[18]Brenner C E,Bucher C.A contribution to the SFE-based reliability assessment of nonlinear structuresunder dynamic loading[J].Probabilistic EngineeringMechanics,1995,10(4):265—273.
[19]陈颖,王东升,朱长春.随机结构在随机载荷下的动力可靠度分析[J].工程力学,2006,23(10):82—85.
[20]李杰,陈建兵.随机结构动力可靠度分析的概率密度演化方法[J].振动工程学报,2004,17(2):121—125.
[21]陈建兵,李杰.复合随机振动系统的动力可靠度分析[J].工程力学,2005,22(3):52—57.
[22]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131—136.
[23]Bucher C G,Bourgund U.A fast and efficient re-sponse surface approach for structural reliability prob-lems[J].Structural Safety,1990,7(1):57—66.
[24]Cressie N.Statistics for Spatial Data[M].NewYork:John Wiley,1993.
[25]Kanai K.Semi-empirical formula for the seismic char-acteristics of the ground motion[J].Bulletin of theEarthquake Research Institute,University of Tokyo,1957,35(2):308—325.
[26]孙广俊,李鸿晶.平稳随机地震地面运动过程模型及其统计特征[J].地震工程与工程振动,2004,24(6):21—26.
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