摘要
预应力是索杆张力结构的最基本结构特性,承担着提供结构刚度和保证结构形态稳定性的作用。作为一类预应力结构,构件长度误差(即索长和杆长误差,以下简称为“长度误差”)是造成索杆张力结构初始形态和初始预张力偏差的最主要因素。如何有效地控制长度误差效应是该类结构设计,特别是施工张拉设计的关键问题。本文主要围绕索杆张力结构的构件长度误差效应,开展了以下三方面的研究工作。
第一、本文给出了构件长度误差效应(包括预张力偏差和形状偏差)分析问题的数学描述,利用不需建立整体刚度矩阵的动力松弛法来进行求解,且采用了悬链线索单元模型及其精确协调方程以确保计算精度。建立了反映预张力偏差和长度误差关系的敏感性矩阵。提出了一种工程中主动张拉索的选取方法。考虑到结构的实际施工成形是以张拉索索力来控制的情况,进一步基于牛顿法提出了存在索力约束条件的长度误差效应求解策略,指出了能否有效控制长度误差效应是评价张拉索方案合理性的重要依据。
第二、针对柔性预张力索杆体系在施工张拉过程中的长度误差敏感性问题,本文采用了Sobol基于方差的敏感性分析方法来进行分析。利用所推导的长度误差敏感性矩阵的解析表达式,对两个不同的索杆张力结构各阶长度误差的敏感性指标进行了计算和分析,比较了不同张拉方案对结构初始预张力的影响。文中还对采用Sobol法进行长度误差敏感性分析的优缺点和有效性进行了讨论。
第三、面向索杆张力结构的实际预张力状态评判及其预张力偏差调整问题,基于遗传算法提出了索杆张力结构最不利索长误差组合的求解策略,以及根据实测初始预张力反求索长误差组合的分析方法。文中还结合一实际工程中的桅杆斜拉悬索系统,利用上述方法进行了最不利索长误差组合的求解以及实测预张力偏差的分析,并对采用遗传算法进行上述问题分析的优缺点及有效性进行了讨论。
Pretension is the basic structural character of cable-strut tensile structures. As a kind of pre-stressed structures, the most important factor of the deviation of the initial shape and initial pre-tension of cable-strut tensile structures is the member length error (cable length error and strut length error, hereinafter referred to as "length error"). How to control the member length error effectively is the key issue in this kind of structural design, especially in the construction tensile design. This paper mainly focuses on the member length error effect of cable-strut tensile structures and carries out the following three aspects of researches.
Firstly, the mathematical description of the length error effects (including the pre-tension deviation and the shape deviation) problems is given, using the Dynamic Relaxation Method without the establishment of the overall stiffness matrix to solve it, and using the catenary cable element model and its precise co-ordination equation to ensure the calculation accuracy. The sensitivity matrix to reflect the relationship between the pre-tension deviation and the length error is established. One method of how to select the initiative cables to pull in project is proposed. Taking into account that the actual construction shaping of the structures is based on controlling the cable tension, the solving strategy of the length error effects which is based on Newton Method with the existence of cable force constraints is further proposed, pointing out that the ability to control the length error effect effectively is an important basis of the evaluation of the reasonableness of cable-tensile program.
Secondly, to solve the sensitivity issue of length error in the pre-tension process of flexible cable-strut tensile system, Sobol's sensitivity analysis method based on variance is used. Using the derived analytical expression of the length error sensitivity matrix to compute and analyse the sensitivity indicators of each order of two different pre-tension cable-strut tensile structures, and comparing the effect of the different programs on initial pre-tension of the structures. The advantages, disadvantages and effectiveness of Sobol's method in length error sensitivity analysis are discussed.
Thirdly, facing the problems of evaluating the actual pre-tension state of cable-strut tensile structures and adjusting the deviationg of the pretension, a strategy based on Genetic Algorithm of solving the worst combination of cable length error of cable-strut tensile structures and a method of analysing how to derive the corresponding combination of cable length error when knowing the measured initial pre-tension is proposed. With a mast cable-stayed suspension system in the actual project, using the method above to solve the worst combination of cable length error and analyse the deviation of the measured pretension, and discussing the advantages, disadvantages and effectiveness of Genetic Algorithm when analyzing the above issues.
引文
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