【作者】 卢波；

【导师】 宋建华；

【作者基本信息】 哈尔滨工业大学 ， 桥梁与隧道工程， 2006， 硕士

【摘要】 近年来大跨度悬链线拱桥在我国得到了广泛应用,随着其跨度的不断增大,稳定问题成为设计和施工中的关键问题。由于施工过程中不确定因素的存在,拱桥将不可避免地产生或大或小的初始几何缺陷。样条函数以其特有的优点可以用来逼近任意的连续曲线,且具有很高的精度。本文中,样条函数一方面被用来逼近各种不同形态和不同幅值大小的初始几何缺陷,另一方面被用来建立空间曲梁的位移函数(即建立样条元)。本文同时考虑几何非线性和材料非线性,采用样条函数方法分析悬链线钢管混凝土拱桥的面内和面外稳定性问题。用3次B样条函数来构造结构的位移模式,先建立了基于样条函数方法的悬链线拱面内、面外一类稳定控制方程,推导了基于样条函数的刚度矩阵和荷载向量,在此基础上利用样条函数模拟任意形态的初始几何缺陷。几何非线性采用总体拉格朗日列式法,在此基础上引入材料非线性的影响推导了初始几何缺陷悬链线拱的双重非线性稳定承载力控制方程。用Matlab编程进行了计算分析。结果表明:(1)随着荷载的增加,具有类似于低阶失稳模态的初始几何缺陷的拱更容易失稳;(2)初始缺陷对稳定性的影响比较明显,施工过程中控制初始缺陷的大小是有必要的;(3)只考虑几何非线性时稳定系数有所降低,但考虑双重非线性时的稳定系数显著降低,说明计入材料非线性的影响是很重要的。更多还原

【Abstract】 Large span catenary arch bridge is becoming more and more popular in recent years. But with the span grows larger and larger, structural stability will be a crucial problem during design and construction process. Due to uncertain factors during construction stage, initial geometrical imperfections can not be avoided.Spline functions can be used to approach arbitrary continuous curves with high accuracy. Here, spline functions are used to approach initial geometrical imperfections with different types and different magnitudes, as well as building spline finite element of 3-D curve beam.In this paper the Spline functions method is used analysis of the in-plane and out-of-plane stability problems for Catenary concrete-filled steel tubular arch bridges, considering the material and geometric nonlinearity. With the cubic B spline functions treated as displacement functions, building stability control equations to solve both out-plane and in-plane stability problems. Deducing inflexibility matrixes and load vectors by spline functions. Initial geometrical imperfections are taken into account in the equations and programs. Geometric nonlinearity adopt total lagrangian formulation, deduce double nonlinearity stability control equations of initial geometrical imperfections catenary arch, with corresponding programs complied in Matlab. The results show that :(1)the types of initial geometry imperfections which are familiar to the first order buckling mode will result in buckling earlier.(2)The infection to stability by initial geometrical imperfections is distinctness. So it’s necessary to control initial geometrical imperfection range during construction stage. (3)The value of the stability factor only decreased a little when taking into account geometrical nonlinearity. But when the geometrical nonlinearity and material nonlinearity are all considered, the value of the stability factor decreased a lot, so considered material nonlinearity is important.更多还原