组合梁斜拉桥的可靠度分析
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摘要
相对于混凝土斜拉桥和钢斜拉桥而言,组合梁斜拉桥具有跨越能力大,自重轻,造价合理,施工进度快,能充分发挥各自材料性能等优点,在近十几年来得到了迅猛的发展。目前对组合梁斜拉桥的研究大部分集中在确定性结构分析方面,但确定性结构分析无法考虑结构参数随机性和作用荷载随机性对结构安全性的影响。将基于概率统计理论的可靠度理论应用于组合梁斜拉桥的结构分析,则可以科学准确地掌握组合梁斜拉桥的安全可靠性。本文以九江重建斜拉桥为工程背景,对多种状态下的组合梁斜拉桥进行了可靠度分析,主要内容包括以下几个方面:
(1)基于Newmark几何模型,将混凝土板和钢梁以及剪力连接件按一整体单元考虑,采用T.L列式增量法,推导了考虑纵向滑移效应的非线性组合梁单元模型;
(2)在推导的非线性组合梁单元模型基础上,根据组合梁的结构特点,利用直接微分法,对组合梁的结构响应梯度进行了计算分析,而后利用改进HL-RF迭代法,由FORM法计算得到可靠度指标,同时编制了基于C++语言以及Matlab程序的组合梁随机有限元程序,并进行了数值算例分析;
(3)利用所编的组合梁随机有限元程序,将随机有限元法直接应用于组合梁斜拉桥施工过程中,对组合梁斜拉桥施工过程的标高控制进行了可靠度分析,并对影响标高控制的参数进行了敏感度分析,得出了一些有益的结论;
(4)由于斜拉索中有较大的索力,在主塔及部分主梁中会产生较大轴压力,此时主塔和主梁应按压弯构件来考虑其极限荷载。按相关方程形式建立了组合梁和塔的极限状态方程,并采用? -约界法作为体系主要模式的识别方法,计算分析了组合梁斜拉桥在承载极限状态下的第一水平和第二水平的体系可靠度;
(5)将支持向量分类机(SVC)和Kriging模型引入到了结构可靠度计算分析中。采用拉丁超立方抽样作为实验设计方法,将SVC/Kriging模型作为响应面函数,同时利用遗传算法进行参数优化,并结合Monte Carlo抽样模拟法,提出了基于SVC/Kriging的改进响应面法,其主要思想为:定义―重要性‖判定函数,在迭代过程中,按判定函数值从抽样样本中选取新的训练样本加入到初始训练样本中,不断更新训练样本,使SVC/Kriging模拟的极限状态方程曲线在MC抽样点分布的区域内能更进一步地快速接近真实极限状态方程曲线。经过数值算例分析,验证了本文方法的准确性、高效性;
(6)桥梁结构对地震响应的非线性和复杂性等问题给可靠度分析带来了较大的困难,相比其他可靠度分析方法,响应面是解决此类问题的有效方法。采用所提的基于SVC/kriging的改进响应面法对随机地震激励下组合梁斜拉桥的首次超越动力可靠度问题进行了计算分析,同时还计算分析了结构参数随机性对可靠度的影响。
Compared to the concrete cable-stayed bridge and steel cable-stayed bridge, the composite beam cable-stayed bridge has the following advantages: long-span capacity, light weight, reasonable cost, short construction period, full use of respective material etc., which has a rapid development in last decade. At present, researches about composite beam cable-stayed bridge are concentrated on the field of deterministic structure analysis, which can’t know how the random structural parameters and random loads impact on the safety of structure. If the reliability theory which based on probability theory is applied to a structural analysis of composite beam cable-stayed bridge, the safety and reliability of composite beam cable-stayed bridge could be controlled scientifically and accurately. The Jiujiang rebuilding cable-stayed bridge is taken as the engineering background, and the reliability of composite beam cable-stayed bridge under various situations is investigated and analyzed, the main contents include the following aspects:
(1) Based on Newmark geometric model, considering the concrete slab、steel beam and shear connectors as a whole element, and making use of the T.L. formulation, a nonlinear composite beam element model was developed which had taken the interface slip effect into consideration;
(2) Based on the nonlinear composite beam element model and the characteristic of composite beam, the structural response gradients of composite beam were obtained by use of the DDM method, meanwhile the reliability index was achieved by use of the FORM method and the improved HL-RF iteration. According to the proposed method, a stochastic finite element program of composite beam written in C++ as well as Matlab was developed. Several numerical examples were computed to validate the accuracy of the proposed approach;
(3) Taking advantage of the proposed stochastic finite element program of composite beam, a stochastic finite element analysis was directly applied to the analysis of composite beam cable-stayed bridge during construction stage,the reliability for elevation control of composite beam during construction stage was analyzed, meanwhile the sensitivity of structure parameter which might have an effect on the elevation control was also analyzed, and some useful conclusions were obtained;
(4) As cables contain huge tensions, which would generate great axial pressure in the bridge tower and part of beams, thus the tower and part of beams should be considered as beam-columns to calculate the ultimate load. The limit state functions of composite beam and tower were developed by using the force-moment interaction equation, and the system reliability both at level 1 and level 2 of the composite beam cable-stayed bridge under the ultimate limit-state was analyzed by using theβ-unzipping method which was used to search the main failure modes;
(5) The support vector classification machine (SVC) and Kriging model were introduced into the study of structure reliability. Based on the experiment design of initial input training sample which was selected by use of the Latin Hypercube Sampling (LHS) method, considering the SVC/Kriging model as the response surface function in which the parameters were optimized by using genetic algorithm, an improved SVC/Kriging–based response surface method was proposed which combined with the Monte Carlo sampling method. The main idea of the proposed method is: choosing some new training points from the test sample according to the value of a defined―important‖critical function during the iterative process, and adding these new training points into the initial training sample to update the whole training sample, finally the approximate limit state function of SVC/Kriging would be more close to the real limit state function within the regions where the Monte Carlo population is located by updating the training sample continuously. Several numerical examples were computed to validate the accuracy and high efficiency of the proposed approach;
(6) The seismic response of bridge structure was characterized by nonlinear and complexity, which caused more difficulties in the reliability analysis. Compared to other reliability methods, the response surface method was regarded as an effective way to solve such problems. Therefore, the proposed improved SVC/Kriging–based response surface method was utilized to analyze the first excursion dynamic reliability issue. Meanwhile, the influence from the randomness of structure parameters was also analyzed.
(1)基于Newmark几何模型,将混凝土板和钢梁以及剪力连接件按一整体单元考虑,采用T.L列式增量法,推导了考虑纵向滑移效应的非线性组合梁单元模型;
(2)在推导的非线性组合梁单元模型基础上,根据组合梁的结构特点,利用直接微分法,对组合梁的结构响应梯度进行了计算分析,而后利用改进HL-RF迭代法,由FORM法计算得到可靠度指标,同时编制了基于C++语言以及Matlab程序的组合梁随机有限元程序,并进行了数值算例分析;
(3)利用所编的组合梁随机有限元程序,将随机有限元法直接应用于组合梁斜拉桥施工过程中,对组合梁斜拉桥施工过程的标高控制进行了可靠度分析,并对影响标高控制的参数进行了敏感度分析,得出了一些有益的结论;
(4)由于斜拉索中有较大的索力,在主塔及部分主梁中会产生较大轴压力,此时主塔和主梁应按压弯构件来考虑其极限荷载。按相关方程形式建立了组合梁和塔的极限状态方程,并采用? -约界法作为体系主要模式的识别方法,计算分析了组合梁斜拉桥在承载极限状态下的第一水平和第二水平的体系可靠度;
(5)将支持向量分类机(SVC)和Kriging模型引入到了结构可靠度计算分析中。采用拉丁超立方抽样作为实验设计方法,将SVC/Kriging模型作为响应面函数,同时利用遗传算法进行参数优化,并结合Monte Carlo抽样模拟法,提出了基于SVC/Kriging的改进响应面法,其主要思想为:定义―重要性‖判定函数,在迭代过程中,按判定函数值从抽样样本中选取新的训练样本加入到初始训练样本中,不断更新训练样本,使SVC/Kriging模拟的极限状态方程曲线在MC抽样点分布的区域内能更进一步地快速接近真实极限状态方程曲线。经过数值算例分析,验证了本文方法的准确性、高效性;
(6)桥梁结构对地震响应的非线性和复杂性等问题给可靠度分析带来了较大的困难,相比其他可靠度分析方法,响应面是解决此类问题的有效方法。采用所提的基于SVC/kriging的改进响应面法对随机地震激励下组合梁斜拉桥的首次超越动力可靠度问题进行了计算分析,同时还计算分析了结构参数随机性对可靠度的影响。
Compared to the concrete cable-stayed bridge and steel cable-stayed bridge, the composite beam cable-stayed bridge has the following advantages: long-span capacity, light weight, reasonable cost, short construction period, full use of respective material etc., which has a rapid development in last decade. At present, researches about composite beam cable-stayed bridge are concentrated on the field of deterministic structure analysis, which can’t know how the random structural parameters and random loads impact on the safety of structure. If the reliability theory which based on probability theory is applied to a structural analysis of composite beam cable-stayed bridge, the safety and reliability of composite beam cable-stayed bridge could be controlled scientifically and accurately. The Jiujiang rebuilding cable-stayed bridge is taken as the engineering background, and the reliability of composite beam cable-stayed bridge under various situations is investigated and analyzed, the main contents include the following aspects:
(1) Based on Newmark geometric model, considering the concrete slab、steel beam and shear connectors as a whole element, and making use of the T.L. formulation, a nonlinear composite beam element model was developed which had taken the interface slip effect into consideration;
(2) Based on the nonlinear composite beam element model and the characteristic of composite beam, the structural response gradients of composite beam were obtained by use of the DDM method, meanwhile the reliability index was achieved by use of the FORM method and the improved HL-RF iteration. According to the proposed method, a stochastic finite element program of composite beam written in C++ as well as Matlab was developed. Several numerical examples were computed to validate the accuracy of the proposed approach;
(3) Taking advantage of the proposed stochastic finite element program of composite beam, a stochastic finite element analysis was directly applied to the analysis of composite beam cable-stayed bridge during construction stage,the reliability for elevation control of composite beam during construction stage was analyzed, meanwhile the sensitivity of structure parameter which might have an effect on the elevation control was also analyzed, and some useful conclusions were obtained;
(4) As cables contain huge tensions, which would generate great axial pressure in the bridge tower and part of beams, thus the tower and part of beams should be considered as beam-columns to calculate the ultimate load. The limit state functions of composite beam and tower were developed by using the force-moment interaction equation, and the system reliability both at level 1 and level 2 of the composite beam cable-stayed bridge under the ultimate limit-state was analyzed by using theβ-unzipping method which was used to search the main failure modes;
(5) The support vector classification machine (SVC) and Kriging model were introduced into the study of structure reliability. Based on the experiment design of initial input training sample which was selected by use of the Latin Hypercube Sampling (LHS) method, considering the SVC/Kriging model as the response surface function in which the parameters were optimized by using genetic algorithm, an improved SVC/Kriging–based response surface method was proposed which combined with the Monte Carlo sampling method. The main idea of the proposed method is: choosing some new training points from the test sample according to the value of a defined―important‖critical function during the iterative process, and adding these new training points into the initial training sample to update the whole training sample, finally the approximate limit state function of SVC/Kriging would be more close to the real limit state function within the regions where the Monte Carlo population is located by updating the training sample continuously. Several numerical examples were computed to validate the accuracy and high efficiency of the proposed approach;
(6) The seismic response of bridge structure was characterized by nonlinear and complexity, which caused more difficulties in the reliability analysis. Compared to other reliability methods, the response surface method was regarded as an effective way to solve such problems. Therefore, the proposed improved SVC/Kriging–based response surface method was utilized to analyze the first excursion dynamic reliability issue. Meanwhile, the influence from the randomness of structure parameters was also analyzed.
引文
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