钢筋混凝土框架结构基于性能和可靠度的抗震优化设计
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摘要
基于可靠度理论的概率极限状态设计法是结构设计的基本法则之一,而新一代"基于性能的地震工程"要求在性能化设计中尚应考虑随机因素的影响。为获得满足预设性能水准和可靠度指标的最优方案,以钢筋混凝土框架结构为例,根据其在不同性能水准下的位移需求,采用非线性随机有限元方法求解结构的抗震可靠度,并将可靠度指标作为约束条件,以总造价为优化目标,提出了一种基于性能和可靠度的抗震优化设计方法。其中,可靠度计算以OpenSees为平台,并采用基于梯度分析的FORM有限元法。优化分析以MATLAB为平台,通过程序调用,实现了与可靠度分析之间的数据通讯。算例分析表明,模拟退火算法在本问题中较遗传算法具有更高全局搜索能力和计算精度。研究成果可为新一代基于性能和可靠度的优化设计提供参考。
The reliability-based limit state design method is one of the main principles in structural design,whereas the new generation performance-based earthquake engineering requires that the random factors should also be taken into account in the performance-based design.In order to obtain the optimal design that satisfies the target performance level and reliability indices,a performance-based and reliability-based seismic design optimization method is proposed.Taking the reinforced concrete frame as an example,the seismic reliability is calculated according to the displacement demands regarding various performance levels,using the nonlinear stochastic finite element method.The target reliabilitiy and the minimum material costs are used as constraints and the objective of the optimization problem,respectively.The first order reliability method(FORM) in conjunction with the nonlinear finite element analysis is adopted for the calculation of reliability indexes,which is made by using the OpenSees program.The design optimization is performed in the MATLAB environment,and uses the OpenSees to realize the data communication.A case study is made and it is observed that the Simulated Annealing algorithm has a higher global search ability and higher accuracy than the Genetic Algorithm in this case.This study provides references to the new generation performance-based and reliability-based seismic design optimization.
The reliability-based limit state design method is one of the main principles in structural design,whereas the new generation performance-based earthquake engineering requires that the random factors should also be taken into account in the performance-based design.In order to obtain the optimal design that satisfies the target performance level and reliability indices,a performance-based and reliability-based seismic design optimization method is proposed.Taking the reinforced concrete frame as an example,the seismic reliability is calculated according to the displacement demands regarding various performance levels,using the nonlinear stochastic finite element method.The target reliabilitiy and the minimum material costs are used as constraints and the objective of the optimization problem,respectively.The first order reliability method(FORM) in conjunction with the nonlinear finite element analysis is adopted for the calculation of reliability indexes,which is made by using the OpenSees program.The design optimization is performed in the MATLAB environment,and uses the OpenSees to realize the data communication.A case study is made and it is observed that the Simulated Annealing algorithm has a higher global search ability and higher accuracy than the Genetic Algorithm in this case.This study provides references to the new generation performance-based and reliability-based seismic design optimization.
引文
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[18]McKenna F,Fenves G L,Scott M H.Open system for earthquake engineering simulation.[Berkeley,CA:University of California,Availablefrom:http://OpenSees.berkeley.edu,2000.
[19]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.OU Jinping,DUAN Yubo,LIU Huiyi.Structural random earthquake action and its statistical parameters[J].J.Harbin Archit.&Civ.Eng.Inst.1994,27(3):1-10.(in Chinese)
[20]吕大刚,宋鹏彦,于晓辉,等.基于矩法的结构非线性整体抗震可靠性分析[J].建筑结构学报,2011(s):119-124.LU Dagang,SONG Pengyan,YU Xiaohui,et al.Nonlinear global seismic reliability analysis of structures based on moment methods[J].Journalof Building Structures(Supplementary Issue 2),119-124.(in Chinese)
[21]Holland J H.Adaptation in natural and artificial systems[M].Cambridge:MIT Press,1992.
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[23]李明.详解MATLAB在最优化计算中的应用[M].北京:电子工业出版社,2011.LI Ming.Details of MATLAB in optimization analysis[M].Beijing:Electronic Industry Press,2011.(in Chinese)
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[2]Applied Technology Council.ATC-40,Seismic Evaluation and Retrofit of Concrete Buildings[S].Red Wood City,California,America:Ap-plied Technology Council,1996.
[3]Federal Emergency Management Agency.FEMA273/FEMA274,NEHRP Commentary on the Guidelines for Seismic RehaBilitation of buildings[S].Washington D C,America:Federal Emergency Management Agency,1996.
[4]GB50011-2010建筑抗震设计规范[S].GB50011-2010 Code for Seismic Design of Buildings[S].(in Chinese)
[5]Stefanou G.The stochastic finite element method:Past,present and future[J].Comput.Methods Appl.Mech.Engrg.2009,198(9-12):1031-1051.
[6]Haukaas T,Der Kiureghian.A finite element reliability and sensitivity methods for performance-based earthquake Engineering[R].PEER Report2003/14,Pacific Earthquake Engineering Research Center,College of Engineering,University of California,Berkeley,April,2004.
[7]Der Kiureghian A,Taylor R L.Numerical methods in structural reliability[C].Proceedings of the ICASP4,Florence,Italy,1983.
[8]Zhang Y,Der Kiureghian.A finite element reliability methods for inelastic structures[R].Report No.UCB/SEMM-97/05,Department of Civiland Environmental Engineering,University of California,Berkeley,CA,1997.
[9]Haldar A,Mahadevan S.Reliability assessment using stochastic finite element analysis[J].John Wiley and Sons,New York,2000.
[10]Frangopol D M,Imai K.Geometrically nonlinear finite element reliability analysis of structural systems.II:applications[J].Computers andStructures,2000,77(6):693-709.
[11]Imai K,Frangopol D M.Geometrically nonlinear finite element reliability analysis of structural systems.I:theory[J].Computers and Structures,2000,77(6):677–691.
[12]GB50011-2001建筑抗震设计规范[S].GB50011-2001 Code for Seismic Design of Buildings[S].(in Chinese)
[13]Melchers R E.Structural Reliability:Analysis and Prediction[J].2nd ed.New York,NY:JohnWiley,1999.
[14]Liu P L,Der Kiureghian.A Multivariate distribution models with prescribed marginal and covariance[J].Probabilistic Engineering Mechanics,1986,1(2):105-112.
[15]Polak E.Optimization:Algorithms and Consistent Approximations(Applied Mathematical Sciences Vol.124)[J].Springer,New York,1997.
[16]Gu Q,Conte J.Convergence studies in nonlinear finite element response sensitivity analysis[C].Proceedings of the Ninth International Confer-ence on Applications of Statistics and Probability in Civil Engineering,ICASP9,San Francisco,California.Eds:A.Der Kiureghian and S.Madanat and J.Pestana,2003.
[17]Franchin P.Reliability of uncertain inelastic structures under earthquake excitation[J].Journal of Engineering Mechanics,2004,130(2):180-191.
[18]McKenna F,Fenves G L,Scott M H.Open system for earthquake engineering simulation.[Berkeley,CA:University of California,Availablefrom:http://OpenSees.berkeley.edu,2000.
[19]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.OU Jinping,DUAN Yubo,LIU Huiyi.Structural random earthquake action and its statistical parameters[J].J.Harbin Archit.&Civ.Eng.Inst.1994,27(3):1-10.(in Chinese)
[20]吕大刚,宋鹏彦,于晓辉,等.基于矩法的结构非线性整体抗震可靠性分析[J].建筑结构学报,2011(s):119-124.LU Dagang,SONG Pengyan,YU Xiaohui,et al.Nonlinear global seismic reliability analysis of structures based on moment methods[J].Journalof Building Structures(Supplementary Issue 2),119-124.(in Chinese)
[21]Holland J H.Adaptation in natural and artificial systems[M].Cambridge:MIT Press,1992.
[22]Michalewicz Z.Genetic algorithms+data structures=evolution programs[M].Berlin:Springer,1998.
[23]李明.详解MATLAB在最优化计算中的应用[M].北京:电子工业出版社,2011.LI Ming.Details of MATLAB in optimization analysis[M].Beijing:Electronic Industry Press,2011.(in Chinese)
[24]Van Laarhoven P J M,Aarts E H L.Simulated annealing:theory and applications[M].Berlin:Springer,1987.
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