钢筋混凝土柱的“强剪弱弯”可靠性区间分析
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摘要
在钢筋混凝土结构抗震设计中,"强剪弱弯"是保证结构延性的一个重要设计概念。引进区间变量表达认知不确定性,对钢筋混凝土框架柱进行失效概率区间分析。通过结合代表认知不确定性的区间变量与代表偶遇不确定性的随机变量完成了对不确定性的数学描述。在此基础上,根据对基本事件的包含关系建立"强剪弱弯"区间可靠性概率模型,并从证据理论出发论证了该失效概率区间的上下界实质上等价于证据理论中的信任与似然函数。对于含有区间值不确定性参数的结构承载力计算,将Berz-Taylor模型引进计算过程中,减少由于区间扩张而导致的误差。在数值模拟计算中,运用模拟退火遗传算法(SAGA)确定了"强剪弱弯"的大致设计区间。根据该设计区间构造了特殊的采样函数进行重要性采样模拟从而得到了失效概率区间。误差分析表明该方法具有较好的精度。最后通过算例分析了各设计因素对"强剪弱弯"可靠性的影响,并提出了相应的设计建议。
In aseismic design of reinforced concrete structures, "strong shear weak bending" is an important design conception to guarantee the ductibility of the structure. The interval variable is introduced to express the epistemic uncertainty and the failure probability interval of reinforced concrete column is analyzed. The mathematic description of uncertainty is fulfilled by integration of the interval variable and random variable that represents the epistemic and aleatory uncertainty, respectively. The interval-valued probabilistic reliability model for "strong shear weak bending" is formulated according to the inclusion relation of the element events and the failure event. The equivalence relation between the belief-plausibility function and the upper-lower boundaries of failure probability interval is verified by the evidence theory as well. For the computation of the resistance capability involving interval-valued uncertain parameters, Berz-Taylor model is introduced to reduce the error induced by interval inflation. The simulated annealing genetic algorithm (SAGA) is applied to determine the approximate design interval of the "strong shear weak bending" in numerical simulation. A specific sampling function constructed by such design interval is adopted to gain the failure probability interval; error analysis indicates that the precision of the method is acceptable. Finally, simulated data analysis is carried out on the different design parameters affecting the reliability and corresponding design suggestions are proposed.
In aseismic design of reinforced concrete structures, "strong shear weak bending" is an important design conception to guarantee the ductibility of the structure. The interval variable is introduced to express the epistemic uncertainty and the failure probability interval of reinforced concrete column is analyzed. The mathematic description of uncertainty is fulfilled by integration of the interval variable and random variable that represents the epistemic and aleatory uncertainty, respectively. The interval-valued probabilistic reliability model for "strong shear weak bending" is formulated according to the inclusion relation of the element events and the failure event. The equivalence relation between the belief-plausibility function and the upper-lower boundaries of failure probability interval is verified by the evidence theory as well. For the computation of the resistance capability involving interval-valued uncertain parameters, Berz-Taylor model is introduced to reduce the error induced by interval inflation. The simulated annealing genetic algorithm (SAGA) is applied to determine the approximate design interval of the "strong shear weak bending" in numerical simulation. A specific sampling function constructed by such design interval is adopted to gain the failure probability interval; error analysis indicates that the precision of the method is acceptable. Finally, simulated data analysis is carried out on the different design parameters affecting the reliability and corresponding design suggestions are proposed.
引文
[1]Oberkampf WL,Helton JC.Mathematical representation of uncertainty[A].Proceeding of the42nd AIAA/ASME/ASCE/AHS/ASC Structures.Structural Dynamics and Materials(SDM)Conference[C].Seattle,2001.
[2]Cremona C,Gao Y.The possibilistic reliability theory:theoretical aspects and applications[J].Structural Safety,1997,19(2):173~201.
[3]Liu Y,Qiao Z,Wang G.Fuzzy random reliability of structures based on fuzzy random variables[J].FuzzySets and Systems,1997,86:345~355.
[4]Moller B,Beer M,Graf W.Fuzzy structural analysis using alpha-level optimization[J].Computational Mechanics,2000,26(6):547~565.
[5]Chen S,Yang X.Interval finite element method for beam structures[J].Finite Elements in Analysis and Design,2000,34:75~88.
[6]Shafer G.A mathematical theory of evidence[M].Princeton:Princeton University Press,1976.
[7]白生翔.适筋混凝土构件配筋界限条件的概率分析[J].建筑结构,1996,5:3~11.Bai Shengxiang.Probability analysis on reinforcement limited condition of under-reinforced concrete member[J].Journal of Building Structures,1996,5:3~11.(in Chinese)
[8]管品武,邹银生,刘立新.反复荷载下钢筋混凝土框架柱抗剪承载力分析[J].世界地震工程,2000,16(2):52~56.Guan Pinwu,Zou Yinsheng,Liu Lixin.Study of ultimate shear strength of reinforced concrete columns under cyclic forces[J].World Information on Earthquake Engineering,2000,16(2):52~56.(in Chinese)
[9]沈在康.混凝土结构设计新规范应用讲评[M].北京:中国建筑工业出版社,1993.Shen Zaikang.Comments on the new code for design of concrete structures[M].Beijing:Architecture Industry Press of China,1993.(in Chinese)
[10]Gotz Alefeld,Gunter Mayer.Interval analysis:theory and applications[J].Journal of Computational and Applied Mathematics,2000,121:421~464.
[11]Berz M.From Taylor series to Taylor models[A].AIP Conference Proceeding[C].1997,405:1~23.
[12]Pezeshk S,Camp CV,Chen D.Design of non-linear framed structures using genetic optimization[J].J.Struct.Engrg,2000,126(3):382~388.
[13]Shun F,He R.Improving real-parameter genetic algorithm with simulated annealing for engineering problems[J].Advances in Engineering Software,2006,37(6):406~418.
[14]Mu S,Su H.A new genetic algorithm to handle the constrained optimization problem[A].Proceedings of the 41st IEEE Conference on Decision and Control[C].Las Vegas,2002.
[2]Cremona C,Gao Y.The possibilistic reliability theory:theoretical aspects and applications[J].Structural Safety,1997,19(2):173~201.
[3]Liu Y,Qiao Z,Wang G.Fuzzy random reliability of structures based on fuzzy random variables[J].FuzzySets and Systems,1997,86:345~355.
[4]Moller B,Beer M,Graf W.Fuzzy structural analysis using alpha-level optimization[J].Computational Mechanics,2000,26(6):547~565.
[5]Chen S,Yang X.Interval finite element method for beam structures[J].Finite Elements in Analysis and Design,2000,34:75~88.
[6]Shafer G.A mathematical theory of evidence[M].Princeton:Princeton University Press,1976.
[7]白生翔.适筋混凝土构件配筋界限条件的概率分析[J].建筑结构,1996,5:3~11.Bai Shengxiang.Probability analysis on reinforcement limited condition of under-reinforced concrete member[J].Journal of Building Structures,1996,5:3~11.(in Chinese)
[8]管品武,邹银生,刘立新.反复荷载下钢筋混凝土框架柱抗剪承载力分析[J].世界地震工程,2000,16(2):52~56.Guan Pinwu,Zou Yinsheng,Liu Lixin.Study of ultimate shear strength of reinforced concrete columns under cyclic forces[J].World Information on Earthquake Engineering,2000,16(2):52~56.(in Chinese)
[9]沈在康.混凝土结构设计新规范应用讲评[M].北京:中国建筑工业出版社,1993.Shen Zaikang.Comments on the new code for design of concrete structures[M].Beijing:Architecture Industry Press of China,1993.(in Chinese)
[10]Gotz Alefeld,Gunter Mayer.Interval analysis:theory and applications[J].Journal of Computational and Applied Mathematics,2000,121:421~464.
[11]Berz M.From Taylor series to Taylor models[A].AIP Conference Proceeding[C].1997,405:1~23.
[12]Pezeshk S,Camp CV,Chen D.Design of non-linear framed structures using genetic optimization[J].J.Struct.Engrg,2000,126(3):382~388.
[13]Shun F,He R.Improving real-parameter genetic algorithm with simulated annealing for engineering problems[J].Advances in Engineering Software,2006,37(6):406~418.
[14]Mu S,Su H.A new genetic algorithm to handle the constrained optimization problem[A].Proceedings of the 41st IEEE Conference on Decision and Control[C].Las Vegas,2002.
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