多维多点地震激励下随机K8单层球面网壳的可靠度分析
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摘要
大跨度空间钢结构的多维多点抗震分析已有不少研究,但针对其随机反应极值分布的研究甚少。传统的基于跨越理论的方法仅在简单的场合和很强的假定下才可得解析解;而扩散过程理论方法仅在单自由度体系等简单情形下才能使用,基于此,将近年来提出的概率密度演化法引入到多维多点激励下大跨度空间钢结构动力反应极值分布的计算中,该法构造了一个虚拟时间过程,建立概率密度演化方程并求解给出随机结构动力反应的极值分布,在安全域内积分即可给出结构动力可靠度。为验证其效率与精度,应用此法求得了多维多点地震激励下单层球面网壳结构的可靠度与极值分布,与随机模拟结果一致,因此引入的算法具有准确、高效和通用的特点。
Although much work has been done on seismic analysis for large span space lattice structures subjected to multi-dimensional multi-support excitations,its extreme value distribution of the stochastic response remains unaddressed.Analytical solutions can be obtained only in simple cases involving strong assumptions using the traditional level-crossing process theory;the diffusion process theory is just feasible for SDOF system.Based on this,the recently developed probability density evolution method is used to capture extreme value of large span space lattice structures subjected to multi-dimensional multi-support excitations.A virtual stochastic process is firstly constructed,then PDEM is built to evaluate extreme value distribution,and dynamic reliability of space structures can be obtained through simple integration.To verify the efficiency and accuracy of the introduced approach,the reliability and extreme value distribution of a long span single layer lattice shell structure under multi-dimensional multi-support excitations are observed.The results agree well with the ones obtained by the stochastic simulation method,so the introduced PDEM is of accuracy,efficiency and versatility.
Although much work has been done on seismic analysis for large span space lattice structures subjected to multi-dimensional multi-support excitations,its extreme value distribution of the stochastic response remains unaddressed.Analytical solutions can be obtained only in simple cases involving strong assumptions using the traditional level-crossing process theory;the diffusion process theory is just feasible for SDOF system.Based on this,the recently developed probability density evolution method is used to capture extreme value of large span space lattice structures subjected to multi-dimensional multi-support excitations.A virtual stochastic process is firstly constructed,then PDEM is built to evaluate extreme value distribution,and dynamic reliability of space structures can be obtained through simple integration.To verify the efficiency and accuracy of the introduced approach,the reliability and extreme value distribution of a long span single layer lattice shell structure under multi-dimensional multi-support excitations are observed.The results agree well with the ones obtained by the stochastic simulation method,so the introduced PDEM is of accuracy,efficiency and versatility.
引文
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[2]李忠献,林伟,丁阳.行波效应对大跨度空间网格结构地震响应的影响[J].天津大学学报,2007,40(1):1―8.Li Zhongxian,Lin Wei,Ding Yang.Influence of wave passage effect on seismic response of long-span spatial lattice structures[J].Journal of Tianjin University,2007,40(1):1―8.(in Chinese)
[3]梁嘉庆,叶继红.结构跨度对非一致输入下大跨度空间网格结构地震响应的影响[J].空间结构,2004,10(3):13―18.Liang Jiaqing,Ye Jihong.The influence of structural span on seismic response of space lattice structures under non-uniform excitation[J].Spatial Structures,2004,10(3):13―18.(in Chinese)
[4]苏亮,董石麟.竖向多点输入下两种典型空间结构的抗震分析[J].工程力学,2007,24(2):85―90.Su Liang,Dong Shilin.Seismic analysis of two typical spatial structures under multi-support vertical excitations[J].Engineering Mechanics,2007,24(2):85―90.(in Chinese)
[5]董贺勋,叶继红.多点输入下大跨空间网格结构的拟静力位移影响因素分析[J].东南大学学报(自然科学版),2005,25(4):574―579.Dong Hexun,Ye Jihong.Effects of some parameters on pseudo-static displacement of space lattice structures under multiple support excitation[J].Journal of Southeast University(Natural Science Edition),2005,25(4):574―579.(in Chinese)
[6]梁嘉庆,叶继红.多点输入下大跨度空间网格结构的地震响应分析[J].东南大学学报(自然科学版),2003,33(5):625―630.Liang Jiaqing,Ye Jihong.Seismic response analysis oflong-span space lattice structures under multiple-supportexcitation[J].Journal of Southeast University,2003,33(5):625―630.(in Chinese)
[7]Heredia Zavoni E,Vanmarke E H.Seismic random-vibration analysis of multi-support-structural systems[J].Eng Mech,1994,120(5):1107―1128.
[8]Kuireghian A D,Neuenhofer A.Response spectrummethod of multi-support seismic excitations[J].Earthquake Engng Struct,Dyn,1992(21):713―740.
[9]Loh C H,Ku B D.An efficient analysis of structuralresponse for multiple-support seismic excitations[J].Engineering Structure,1995,17(1):15―26.
[10]白学丽.多维多点输入下大跨空间网格结构地震响应及构件可靠度分析[D].南京:东南大学,2006.Bai Xueli.Seismic behavior and element reliability ofspace lattice structures under multi-dimensional andmulti-support excitations[D].Nanjing:SoutheastUniversity,2006.(in Chinese)
[11]陈建兵,李杰.随机结构动力反应的极值分布[J].振动工程学报,2004,17(4):382―387.Chen Jianbing,Li Jie.Extreme value distribution of thedynamic response for stochastic structures[J].Journal ofVibration Engineering,2004,17(4):382―387.(inChinese)
[12]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 Jianbing,Li Jie.The extreme value probabilitydensity function based method for dynamic reliabilityassessment of stochastic structures[J].EarthquakeEngineering and Engineering Vibration,2004,24(6):39―44.(in Chinese)
[13]张文生.科学计算中的偏微分方程有限差分法[M].北京:高等教育出版社,2006.Zhang Wensheng.Partial differential finite differencemethod in scientific computation[M].Beijing:HigherEducation Press,2006.(in Chinese)
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