钢框架结构的非线性静力抗震可靠性分析 II:可靠度指标及其灵敏度
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摘要
将有限元反应及其灵敏度分析与结构可靠度分析的近似解析方法结合起来,可以进行具有隐式功能函数的大型复杂结构的可靠性分析。在基于位移的非线性纤维梁柱单元及其灵敏度直接微分表达式的基础上,通过力学变换、概率变换和反应灵敏度,将结构可靠度计算方法FORM和SORM与有限元方法有机地集成在一起。依据现行抗震设计规范,建立了钢框架结构典型构件承载能力和结构层间变形能力的抗震极限状态方程,利用地震作用的等效随机静力模型,采用非线性有限元静力可靠度方法,对一实际工程结构的抗震可靠度及其灵敏度进行了概率分析和评价,结果表明:尽管在大震作用下该结构的层间弹塑性变形可靠度较高,但是构件极限承载能力的可靠度指标较低,仍然存在失效的可能性。因此,仅验算"小震"作用下结构的承载能力可靠度和"大震"作用下结构的变形能力可靠度是不够的,还需要验算在"中震"和"大震"作用下结构的极限承载能力可靠度。
The reliability analysis of large-scale complex structures with implicit performance functions can be realized by combining the finite element response and its sensitivity analysis with the approximate analytical methods in structural reliability theory.In this companion paper,the finite element methods and computational reliability methods including FORM and SORM are efficiently integrated by mechanical transformation,probability transformation and response sensitivity analysis based on the theory of nonlinear displacement fiber beam-column element and direct differential response sensitivity formulations.According to the current seismic design code,the seismic limit state functions of strength and displacement are built up for typical members and storey levels of steel frames.Based on the equivalent static model of the random seismic action,the seismic reliability and its sensitivities of a practical engineering structure is analyzed by the nonlinear finite element reliability method.The results show that although the reliability index for storey-level displacement is high under the action of severe earthquakes,the strength reliability index is very low.This reveals that the structure is still at the high risk of failure.Therefore,it is not sufficient to check the load-carrying capacity reliability under minor earthquakes and deformation reliability under major earthquakes.It is necessary to verify the ultimate load-carrying capacity reliability under both moderate and major earthquakes.
The reliability analysis of large-scale complex structures with implicit performance functions can be realized by combining the finite element response and its sensitivity analysis with the approximate analytical methods in structural reliability theory.In this companion paper,the finite element methods and computational reliability methods including FORM and SORM are efficiently integrated by mechanical transformation,probability transformation and response sensitivity analysis based on the theory of nonlinear displacement fiber beam-column element and direct differential response sensitivity formulations.According to the current seismic design code,the seismic limit state functions of strength and displacement are built up for typical members and storey levels of steel frames.Based on the equivalent static model of the random seismic action,the seismic reliability and its sensitivities of a practical engineering structure is analyzed by the nonlinear finite element reliability method.The results show that although the reliability index for storey-level displacement is high under the action of severe earthquakes,the strength reliability index is very low.This reveals that the structure is still at the high risk of failure.Therefore,it is not sufficient to check the load-carrying capacity reliability under minor earthquakes and deformation reliability under major earthquakes.It is necessary to verify the ultimate load-carrying capacity reliability under both moderate and major earthquakes.
引文
[1]Ghanem R G,Spanos P D.Stochastic finite elements:A spectral approach[M].New York:Springer-Verlag,1991.
[2]Kleiber M,Hien TD.The Stochastic finite elements[M].New York:John Wiley&Sons,1992.
[3]陈虬,刘先斌.随机有限元法及其工程应用[M].成都:西南交通大学出版社,1993.
[4]秦权.随机有限元及其进展I:随机场的离散和反应矩的计算[J].工程力学,1994,11(4):1-10.
[5]李杰.随机结构系统—分析与建模[M].北京:科学出版社,1996.
[6]武清玺.结构可靠性分析及随机有限元法[M].北京:机械工业出版社,2005.
[7]安伟光,蔡荫林,陈卫东.随机结构系统可靠性分析与优化设计[M].哈尔滨:哈尔滨工程大学出版社,2005.
[8]吴世伟.结构可靠度分析[M].北京:人民交通出版社,1990.
[9]秦权.随机有限元及其进展II:可靠度随机有限元和随机有限元的应用[J].工程力学,1995,12(1):1-9.
[10]刘宁.可靠度随机有限元法及其工程应用[M].北京:中国水利水电出版社,2001.
[11]秦权,林道锦,梅刚.结构可靠度随机有限元—理论及工程应用[M].北京:清华大学出版社,2006.
[12]Der Kiureghian A,Ke J-B.The stochastic finite element method in structural reliability[J].Probabilistic Engineering Mechanics,1988,3(2):83-91.
[13]吕大刚.论结构可靠度理论中的概率变换[C]//中国力学学会学术大会2005,北京,2005.10.
[14]吕大刚.基于线性化Nataf变换的一次可靠度方法[J].工程力学,2007,24(5):79-86.
[15]Zhang Y,Der Kiureghian A.Two improved algorithms for reliability analysis.In Reliability and Optimization of Structural Systems[C]//Pro-ceedings of the 6th IFI PWG7.5 working conference on Reliability and Optimization of Structural systems,1994,(eds R.Rackwitz,G.,Augus-ti,A.Borrri),297-304.
[16]吕大刚,李晓鹏,胡晓琦,等.钢框架结构的非线性静力抗震可靠性分析I.有限元反应及其灵敏度[J].地震工程与工程振动,2007,27(5):55-60.
[17]李晓鹏,吕大刚.基于FORM的有限元可靠度方法及其应用[J].哈尔滨工业大学学报,2005(增刊):60-63.
[18]Melchers R E.Structural reliability:analysis and prediction[M].New York:NY.2nd Edition,John Wiley,1999.
[19]吕大刚,李晓鹏.钢框架结构抗震可靠性的概率重要度分析[J].建筑结构学报,2007.
[20]欧进萍,段宇博,刘会仪.结构随机地震作用及其统计参数[J].哈尔滨建筑工程学院学报,1994,27(5):1-10.
[21]宋曼华.钢结构设计与计算[M].北京:机械工业出版社,2000.
[22]胡晓琦.钢框架结构地震损伤可靠度分析与抗震性能设计研究[D].哈尔滨:哈尔滨工业大学,2005.
[23]李晓鹏.基于FORM的钢框架结构抗震可靠度与地震易损性分析[D].哈尔滨:哈尔滨工业大学,2005.
[2]Kleiber M,Hien TD.The Stochastic finite elements[M].New York:John Wiley&Sons,1992.
[3]陈虬,刘先斌.随机有限元法及其工程应用[M].成都:西南交通大学出版社,1993.
[4]秦权.随机有限元及其进展I:随机场的离散和反应矩的计算[J].工程力学,1994,11(4):1-10.
[5]李杰.随机结构系统—分析与建模[M].北京:科学出版社,1996.
[6]武清玺.结构可靠性分析及随机有限元法[M].北京:机械工业出版社,2005.
[7]安伟光,蔡荫林,陈卫东.随机结构系统可靠性分析与优化设计[M].哈尔滨:哈尔滨工程大学出版社,2005.
[8]吴世伟.结构可靠度分析[M].北京:人民交通出版社,1990.
[9]秦权.随机有限元及其进展II:可靠度随机有限元和随机有限元的应用[J].工程力学,1995,12(1):1-9.
[10]刘宁.可靠度随机有限元法及其工程应用[M].北京:中国水利水电出版社,2001.
[11]秦权,林道锦,梅刚.结构可靠度随机有限元—理论及工程应用[M].北京:清华大学出版社,2006.
[12]Der Kiureghian A,Ke J-B.The stochastic finite element method in structural reliability[J].Probabilistic Engineering Mechanics,1988,3(2):83-91.
[13]吕大刚.论结构可靠度理论中的概率变换[C]//中国力学学会学术大会2005,北京,2005.10.
[14]吕大刚.基于线性化Nataf变换的一次可靠度方法[J].工程力学,2007,24(5):79-86.
[15]Zhang Y,Der Kiureghian A.Two improved algorithms for reliability analysis.In Reliability and Optimization of Structural Systems[C]//Pro-ceedings of the 6th IFI PWG7.5 working conference on Reliability and Optimization of Structural systems,1994,(eds R.Rackwitz,G.,Augus-ti,A.Borrri),297-304.
[16]吕大刚,李晓鹏,胡晓琦,等.钢框架结构的非线性静力抗震可靠性分析I.有限元反应及其灵敏度[J].地震工程与工程振动,2007,27(5):55-60.
[17]李晓鹏,吕大刚.基于FORM的有限元可靠度方法及其应用[J].哈尔滨工业大学学报,2005(增刊):60-63.
[18]Melchers R E.Structural reliability:analysis and prediction[M].New York:NY.2nd Edition,John Wiley,1999.
[19]吕大刚,李晓鹏.钢框架结构抗震可靠性的概率重要度分析[J].建筑结构学报,2007.
[20]欧进萍,段宇博,刘会仪.结构随机地震作用及其统计参数[J].哈尔滨建筑工程学院学报,1994,27(5):1-10.
[21]宋曼华.钢结构设计与计算[M].北京:机械工业出版社,2000.
[22]胡晓琦.钢框架结构地震损伤可靠度分析与抗震性能设计研究[D].哈尔滨:哈尔滨工业大学,2005.
[23]李晓鹏.基于FORM的钢框架结构抗震可靠度与地震易损性分析[D].哈尔滨:哈尔滨工业大学,2005.
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