索杆张力结构最不利预张力偏差的近似解析方法  

AN APPROXIMATE ANALYTICAL METHOD FOR UNFAVORABLE PRETENSION DEVIATIONS OF CABLE-BAR TENSILE STRUCTURES

作　　者：夏巨伟[1] 邓华[1] 

机构地区：[1]浙江大学空间结构研究中心,浙江杭州310058

出　　处：《工程力学》2015年第6期8-14,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(50978226)

摘　　要：索杆张力结构需依靠预张力来获得初始刚度和维持稳定性,但实际工程中索长误差等因素所引起的预张力偏差不可忽视。分别以单元绝对和相对预张力偏差平方和作为结构预张力偏差的评价指标,建立了两类指标与索长误差间的二次型解析表达式。利用其中二次型矩阵Rayleigh商的极性解释了结构最不利预张力偏差的有界性。进一步对二次型矩阵进行谱分解,将结构最不利预张力偏差表示为以该矩阵特征值为权重、以索长误差在特征向量上的投影值为因子的加权平方和形式。发现二次型矩阵的特征值衰减迅速,故近似采用其一阶特征值和特征向量便能有效估计结构的最不利预张力偏差大小以及对应的索长误差分布。采用该文方法对一个实际索杆张力结构的最不利预张力偏差进行求解,并与两种常规优化算法的计算结果进行对比考察了该方法的计算精度和有效性。Cable-bar tensile structures require pretension to establish initial stiffness and stability. Hence, the pretension deviation resulted from such factors as the cable length errors cannot be ignored in engineering practice. Adopting the quadratic sum of the absolute and relative pretension deviations as the quantitative indices of structural pretension deviation, the analytical relationships between these two indices and the cable length errors are expressed in quadratic forms. By means of the polarity of the Rayleigh quotient of its quadratic matrix, the boundedness of unfavorable structural pretension deviation(MUSPD) is proved. Through a spectral decomposition, the MUSPD is expressed in the form of weighting quadratic summation, with the eigenvalues of the quadratic matrix being the weights and the projection of the cable length errors on eigenvectors being the factors. Due to the rapid attenuation of the eigenvalues, the MUSPD as well as the corresponding distribution of cable length errors can be approximated by adopting first-order eigenvalues and eigenvectors. The MUSPD of a practical cable-strut tensile structure is calculated using the proposed method, with its accuracy and validity investigated by comparing with two conventional optimization algorithms.

关 键 词：索杆张力结构 构件长度误差 最不利预张力偏差 RAYLEIGH商 谱分解 

分 类 号：TU399[建筑科学—结构工程]