索杆张力结构的预张力偏差和刚度解析
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摘要
本文以索杆张力结构为研究对象,重点对其预张力偏差的定量估计和控制、刚度解析问题进行了讨论,主要工作包括以下五个方面：
(1)对结构的最不利预张力偏差问题进行了研究。以构件绝对和相对预张力偏差平方和作为衡量结构预张力偏差的指标,利用二次型矩阵Rayleigh商的极性对结构预张力偏差的有界性进行了证明。通过对该二次型矩阵进行谱分解并利用其特征值快速衰减的性质,建立了仅采用该矩阵的低阶特征值和特征向量来近似求解结构最不利预张力偏差及对应的索长误差分布的方法。
(2)以控制结构预张力偏差为目标讨论了主动张拉索的优选问题。将单元的绝对预张力偏差平方和作为表征结构预张力偏差的定量指标,从特征值的角度解释了不同张拉方案对结构预张力偏差控制效果不同的原因。以灵敏度矩阵的第一阶特征值为评价指标,从控制结构整体最不利预张力偏差的角度基于遗传算法提出了一种主动张拉索的优选方法。
(3)结合乐清市体育场月牙形索桁张力罩棚结构工程,从预张力偏差的角度开展了施工张拉方案的比选和结构预张力的实测工作。对该结构在不同张拉控制方案下的结构预张力偏差进行了分析,并建议了可行的预张力施工方案。介绍了该结构的预张力监测方案,并将FBG和EM两种索力测量方法应用于该结构的预张力监测并建立了适应长期运行的实时索力监测系统。分析了该结构张拉过程及初始态的实测预张力特点。
(4)重点对单元刚度与结构需求刚度间的关系进行了研究。给出了一个新的结构切线刚度矩阵按单元组集的表达式,其中结构的弹性刚度矩阵和几何刚度矩阵均可表示成为刚度值和方向向量构成的解析形式。在理论上找到了两个重要的结构自由度子空间,零弹性刚度子空间和需求刚度子空间,零弹性刚度子空间的刚度主要由结构的几何刚度提供,需求刚度子空间的刚度为外荷载作用方向的结构刚度。建立了结构和单元刚度对需求刚度和零弹性刚度子空间刚度贡献度的量化方法,通过该方法可找到结构的关键刚度路径。
(5)对结构的动力刚度特性进行了初步探讨。建立了结构基本模态参数(频率和振型)与单元弹性刚度和几何刚度之间的关系。发现索杆张力结构的频谱视几何刚度和弹性刚度对各阶频率贡献度大小的不同存在明显的“分区现象”,并给出了定量判别结构各阶频率中几何刚度、弹性刚度贡献度的方法。利用零弹性模态子空间的刚度主要由几何刚度提供的特点,根据单元几何刚度对其刚度贡献度的大小建立了一个寻找结构关键预张力单元的方法。最后建立了频率、振型与结构预张力间的解析关系,借助该关系式可根据实测的模态参数来求解结构预张力。
The paper takes cable-strut tensile structures as the research object, focusing on the quantitative estimation and control of its pretension deviation, stiffness analysis problem. The main works include the following five aspects:
(1) The most unfavorable structural pretension deviation (MUSPD) is studied. Adopting the quadratic sum of member's absolute and relative pretension deviations as the quantitative indices of structural pretension deviation, the MUSPD is proved to be bounded by means of the polarity of Rayleigh quotient of the quadratic matrix. By the spectral decomposition of the quadratic matrix and taking advantage of the steep attenuation of its eigenvalues, the method utilizing only its first-order eigenvalue and eigenvector to approximately solve the MUSPD as well as the corresponding distribution of cable length errors is established.
(2) Aimed at controlling structural pretension deviation, the problem of choosing the optimal actively-stretched cables is discussed. The quadratic sum of elemental pretension deviations is adopted as an index to evaluate the pretension deviation of the whole structure, the reason is expounded that different stretch schemes lead to different control effect of structural pretension deviation from the perspective of eigenvalues. Adopting the first-order eigenvalue of the sensitivity matrix as the evaluating indicator, from the perspective of controlling the MUSPD, an optimization algorithm for choosing actively-stretched cables is put forward based on the Genetic Algorithm.
(3) Combined with the crescent-shaped cable-truss tensile canopy structure of Yueqing Stadium, comparison of construction stretch schemes as well as measurement of structural pretension are carried out from the perspective of structural pretension deviation. The structural pretension deviations of different stretch-control schemes are analyzed and the feasible pretension construction scheme is proposed. The cable force monitoring scheme is introduced, the FBG and EM methods are applied to monitor cable forces and a long-term real-time monitoring system is established. In addition, the characteristics of structural pretension during the stretch process and the initial state are analyzed as well.
(4) The research is focused on the relationship between element stiffness and structure demand stiffness. A new expression of structure tangent stiffness matrix is given, in which both element stiffness matrix and element geometric stiffness matrix can be expressed as the analytical form of its stiffness value and the corresponding direction vector. Two important structural freedom subspaces, demand stiffness subspace(DSS) and zero elastic stiffness subspace(ZESS) are discovered theoretically. The stiffness of ZESS is mainly offered by geometric stiffness while the stiffness of DSS is the structure stiffness in the direction of external load. The methods of quantifying the stiffness contribution of structural and elemental stiffness to DSS and ZESS are established, by which the key stiffness path of the structure can be found.
(5) The dynamic stiffness characteristics of the structure are discussed preliminarily. The relationship between two basic structural modal parameters (frequency and mode) and element elastic stiffness and element geometric stiffness is established. The frequency spectrum of cable-strut tensile structure is found to have an obvious'partition phenomenon'depending on the contribution of geometric stiffness and elastic stiffness to frequencies, and a method is established to distinguish quantificationally the contribution of geometric stiffness and elastic stiffness to some frequency. Using the characteristics that the stiffness of zero elastic modal subspace mainly comes from the contribution of geometric stiffness, a method to find the key pretension elements is set up according to the contribution of element geometric stiffness. Finally, the analytical relationship of frequency, mode and pretension is established, with the help of which the structural pretension can be solved by the measured modal parameters.
(1)对结构的最不利预张力偏差问题进行了研究。以构件绝对和相对预张力偏差平方和作为衡量结构预张力偏差的指标,利用二次型矩阵Rayleigh商的极性对结构预张力偏差的有界性进行了证明。通过对该二次型矩阵进行谱分解并利用其特征值快速衰减的性质,建立了仅采用该矩阵的低阶特征值和特征向量来近似求解结构最不利预张力偏差及对应的索长误差分布的方法。
(2)以控制结构预张力偏差为目标讨论了主动张拉索的优选问题。将单元的绝对预张力偏差平方和作为表征结构预张力偏差的定量指标,从特征值的角度解释了不同张拉方案对结构预张力偏差控制效果不同的原因。以灵敏度矩阵的第一阶特征值为评价指标,从控制结构整体最不利预张力偏差的角度基于遗传算法提出了一种主动张拉索的优选方法。
(3)结合乐清市体育场月牙形索桁张力罩棚结构工程,从预张力偏差的角度开展了施工张拉方案的比选和结构预张力的实测工作。对该结构在不同张拉控制方案下的结构预张力偏差进行了分析,并建议了可行的预张力施工方案。介绍了该结构的预张力监测方案,并将FBG和EM两种索力测量方法应用于该结构的预张力监测并建立了适应长期运行的实时索力监测系统。分析了该结构张拉过程及初始态的实测预张力特点。
(4)重点对单元刚度与结构需求刚度间的关系进行了研究。给出了一个新的结构切线刚度矩阵按单元组集的表达式,其中结构的弹性刚度矩阵和几何刚度矩阵均可表示成为刚度值和方向向量构成的解析形式。在理论上找到了两个重要的结构自由度子空间,零弹性刚度子空间和需求刚度子空间,零弹性刚度子空间的刚度主要由结构的几何刚度提供,需求刚度子空间的刚度为外荷载作用方向的结构刚度。建立了结构和单元刚度对需求刚度和零弹性刚度子空间刚度贡献度的量化方法,通过该方法可找到结构的关键刚度路径。
(5)对结构的动力刚度特性进行了初步探讨。建立了结构基本模态参数(频率和振型)与单元弹性刚度和几何刚度之间的关系。发现索杆张力结构的频谱视几何刚度和弹性刚度对各阶频率贡献度大小的不同存在明显的“分区现象”,并给出了定量判别结构各阶频率中几何刚度、弹性刚度贡献度的方法。利用零弹性模态子空间的刚度主要由几何刚度提供的特点,根据单元几何刚度对其刚度贡献度的大小建立了一个寻找结构关键预张力单元的方法。最后建立了频率、振型与结构预张力间的解析关系,借助该关系式可根据实测的模态参数来求解结构预张力。
The paper takes cable-strut tensile structures as the research object, focusing on the quantitative estimation and control of its pretension deviation, stiffness analysis problem. The main works include the following five aspects:
(1) The most unfavorable structural pretension deviation (MUSPD) is studied. Adopting the quadratic sum of member's absolute and relative pretension deviations as the quantitative indices of structural pretension deviation, the MUSPD is proved to be bounded by means of the polarity of Rayleigh quotient of the quadratic matrix. By the spectral decomposition of the quadratic matrix and taking advantage of the steep attenuation of its eigenvalues, the method utilizing only its first-order eigenvalue and eigenvector to approximately solve the MUSPD as well as the corresponding distribution of cable length errors is established.
(2) Aimed at controlling structural pretension deviation, the problem of choosing the optimal actively-stretched cables is discussed. The quadratic sum of elemental pretension deviations is adopted as an index to evaluate the pretension deviation of the whole structure, the reason is expounded that different stretch schemes lead to different control effect of structural pretension deviation from the perspective of eigenvalues. Adopting the first-order eigenvalue of the sensitivity matrix as the evaluating indicator, from the perspective of controlling the MUSPD, an optimization algorithm for choosing actively-stretched cables is put forward based on the Genetic Algorithm.
(3) Combined with the crescent-shaped cable-truss tensile canopy structure of Yueqing Stadium, comparison of construction stretch schemes as well as measurement of structural pretension are carried out from the perspective of structural pretension deviation. The structural pretension deviations of different stretch-control schemes are analyzed and the feasible pretension construction scheme is proposed. The cable force monitoring scheme is introduced, the FBG and EM methods are applied to monitor cable forces and a long-term real-time monitoring system is established. In addition, the characteristics of structural pretension during the stretch process and the initial state are analyzed as well.
(4) The research is focused on the relationship between element stiffness and structure demand stiffness. A new expression of structure tangent stiffness matrix is given, in which both element stiffness matrix and element geometric stiffness matrix can be expressed as the analytical form of its stiffness value and the corresponding direction vector. Two important structural freedom subspaces, demand stiffness subspace(DSS) and zero elastic stiffness subspace(ZESS) are discovered theoretically. The stiffness of ZESS is mainly offered by geometric stiffness while the stiffness of DSS is the structure stiffness in the direction of external load. The methods of quantifying the stiffness contribution of structural and elemental stiffness to DSS and ZESS are established, by which the key stiffness path of the structure can be found.
(5) The dynamic stiffness characteristics of the structure are discussed preliminarily. The relationship between two basic structural modal parameters (frequency and mode) and element elastic stiffness and element geometric stiffness is established. The frequency spectrum of cable-strut tensile structure is found to have an obvious'partition phenomenon'depending on the contribution of geometric stiffness and elastic stiffness to frequencies, and a method is established to distinguish quantificationally the contribution of geometric stiffness and elastic stiffness to some frequency. Using the characteristics that the stiffness of zero elastic modal subspace mainly comes from the contribution of geometric stiffness, a method to find the key pretension elements is set up according to the contribution of element geometric stiffness. Finally, the analytical relationship of frequency, mode and pretension is established, with the help of which the structural pretension can be solved by the measured modal parameters.
引文
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