复杂边界条件下索结构的内力识别方法研究

发布时间：2018-03-23 17:42

本文选题：缆索体系　切入点：索力识别方法　出处：《华南理工大学》2015年博士论文

【摘要】：随着一系列缆索减振方法的应用,索结构的边界条件愈发复杂,给其内力的识别增加了难度,传统的方法在应用于复杂边界条件时,将带来难以估计的误差,因此对复杂边界条件下拉索结构的内力识别方法进行研究势在必行。本文结合大跨缆索承重体系桥梁索力识别中的难点问题,对两端固支、中间弹性多支承、带减振架等复杂边界条件下索结构的内力识别方法进行了深入系统的研究,主要完成了以下工作:(1)基于拉索横向振动方程通解,推导出了可用于多种边界条件的索杆内力计算的统一实用公式,该公式只需在弦理论索力计算公式的基础上乘以修正系数nK,且可采用多阶频率进行索力计算。具有形式简洁、精度高、误差可预知性、可显式计算拉索截面抗弯刚度等优点,工程应用简便且精度可靠。(2)结合动态刚度矩阵法的思想,选择随频率变化的动态单元位移模式,推导了单元刚度矩阵和质量矩阵,构造了用于索力识别的精确动态梁单元,编制了基于该单元的拉索内力识别程序。通过与常规梁单元的对比可知,本文提出的索力识别方法具有精度高、计算耗时少等明显优势。(3)基于能量变分原理,采用本文提出的精确动态梁单元,提出了多弹性支承拉索索力的有限元计算方法。该方法可以充分考虑各种复杂边界条件的影响,突破了既有方法只能计算简支或固支边界条件的局限性,可考虑减震器的减振刚度、转向块、护筒(护套)的作用及多点弹性支承边界的影响。室内试验和实际工程测试结果均表明该方法具有较高的精度。(4)采用稳定函数作为单元的横向位移插值函数,构造了一种空间两节点梁单元,并提出了减振架刚度和质量的等效方法,通过等效处理,既简化了带减振架吊索系统的有限元模型,又如实反映了系统内各构件之间的相互作用,确保了索力识别的精度。最后编制了相应的内力识别程序。通过对两座大跨度悬索桥实际工程的吊索索力进行实测,结果表明本文方法精度高且实用性强。(5)从悬索微段的力学平衡原理出发,通过求解单元的平衡微分方程得到了单元刚度矩阵的解析表达式,构造了一种可用于悬索找形的精确悬链线单元,提出了以“形”找“力”的新方法,编制了相应的吊索内力识别程序,可对所有吊索的内力一次性识别。算例验证结果表明与常规频率法相比,本文方法更高效,可实现主缆线形与吊索索力的同步监测。
[Abstract]:With the application of a series of cable damping methods, the boundary conditions of cable structures become more and more complex, which makes it more difficult to identify the internal forces. The traditional methods will bring inestimable errors when they are applied to complex boundary conditions. Therefore, it is imperative to study the identification method of internal force of cable structure with complex boundary conditions. In this paper, combined with the difficult problems in the identification of cable force of long-span cable bearing system bridge, the two ends are fixed, and the middle elastic multi-support is used. The identification method of internal force of cable structure with vibration absorber and other complex boundary conditions is studied systematically. The following work is accomplished: 1) based on the general solution of cable lateral vibration equation, A unified and practical formula for calculating the internal force of cable rod with various boundary conditions is derived. The formula only needs to be multiplied by the modified coefficient nK on the basis of the formula of cable force calculation in string theory, and the calculation of cable force can be carried out with multi-order frequency. The formula is simple in form. It has the advantages of high precision, predictable error, explicit calculation of bending stiffness of cable section, and so on. It is simple in engineering application and reliable in accuracy. Combined with the idea of dynamic stiffness matrix method, the dynamic element displacement mode varying with frequency is selected. The stiffness matrix and mass matrix of the element are derived, the precise dynamic beam element for cable force identification is constructed, and the program of cable internal force identification based on the element is developed. The cable force identification method presented in this paper has obvious advantages such as high precision, less calculation time, etc.) based on the energy variational principle, the precise dynamic beam element proposed in this paper is adopted. A finite element method for the calculation of cable forces with multiple elastic supports is presented. The method can fully consider the influence of various complex boundary conditions and breaks through the limitations of the existing methods which can only calculate simply supported or fixed supported boundary conditions. May consider the shock absorber's vibration absorption stiffness, the steering block, The effect of sheathing (sheathing) and the influence of multi-point elastic support boundary. The results of indoor test and practical engineering test show that the method has a high precision. The stability function is used as the lateral displacement interpolation function of the element. A kind of spatial two-node beam element is constructed, and the equivalent method of stiffness and mass of vibration absorber is put forward. By equivalent treatment, the finite element model of suspension system with damping frame is simplified. It also reflects the interaction among the components of the system and ensures the accuracy of cable force identification. Finally, a corresponding internal force identification program is worked out. The actual cable force of two long-span suspension bridges is measured. The results show that the method is accurate and practical. (5) based on the mechanical equilibrium principle of the micro segment of the suspension cable, the analytical expression of the element stiffness matrix is obtained by solving the equilibrium differential equation of the element. An accurate catenary element for finding the shape of suspension cable is constructed. A new method of finding "force" by "shape" is proposed, and a corresponding program for identifying the internal force of sling is developed. The numerical results show that the proposed method is more efficient than the conventional frequency method and can realize the synchronous monitoring of the main cable shape and the cable force.
【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：U446

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