自锚式悬索桥索力优化的双矩阵法

Double matrix method for optimizing cable force of self-anchored suspension bridge

为了确定自锚式悬索桥在目标优化状态下的最优索力,针对传统影响矩阵法进行索力优化时需要多次迭代计算、对初始条件敏感等问题,提出索力优化双矩阵法。首先,考虑主梁存在巨大轴力的结构特点,根据恒载、初始索力与加劲梁内力确定结构初始刚度,经过非线性有限元计算,利用叠加原理得到自锚式悬索桥的2个影响矩阵;随后,基于影响矩阵基本理论,推导矩阵方程,建立结构内力状态与位移状态间的关系,求解矩阵方程可得指定约束条件下的目标索力,通过算例阐明双矩阵法的主要计算过程,并将双矩阵法与传统影响矩阵法进行对比,分析迭代过程并讨论初始施调索力的影响;最后,以三跨自锚式悬索桥为例,应用双矩阵法实现索力优化。研究结果表明:算例中双矩阵法与传统影响矩阵法的计算结果相对偏差最大为0.14%;双矩阵法通过矩阵方程直接建立缆索内力与位移约束条件间的关系,其本质是结构内力与变形间的线性关系,因此无需进行迭代计算;双矩阵法不需要限定初始施调索力与索力施加方式,避免了传统影响矩阵法受初始索力影响导致的无法收敛等问题;此外,根据实际应用中索力优化的不同情况,双矩阵法中的位移约束条件可拓展为塔梁弯矩、截面应力等约束条件,便于在大跨度悬索桥设计中应用。

In order to determine the optimal cable force of a self-anchored suspension bridgeunder the target optimization state,aiming at the problems of the traditional influence matrixmethod for cable force optimization,which requires multiple iteration calculations and issensitive to the initial conditions,the double-matrix method was proposed to optimize cableforce.Firstly,considering the structural characteristics of the main girder with huge axialforce,the initial stiffness of the structure was determined according to the dead load,theinitial cable force and the internal force of the stiffening girder.After nonlinear finite elementcalculations,two influence matrices of the self-anchored suspension bridge were obtainedusing the superposition principle.Subsequently,based on the basic theory of the influencematrix,the matrix equation was deduced,and the relationship between internal force state anddisplacement state of the structure was established.The matrix equation was solved to obtainthe target cable force under the specified constraint conditions.Through a calculationexample,the main process of the double matrix method was explained,and the double matrixmethod was compared with the traditional influence matrix method to analyze the iterativeprocess and discuss the impact of initial cable force application.Finally,a three-spanself-anchored suspension bridge was taken as an example,the double matrix method was applied tooptimize the cable force.The results show that the maximum relative difference between thecalculation results of the double matrix method and the traditional influence matrix method inthe calculation example is 0.14%.The double matrix method directly establishes therelationship between cable internal force and displacement constraint through the matrixequation,and its essence is the linear relationship between structural internal force anddeformation.Therefore,no iterative calculation is required.The double matrix method doesnot need to limit the initial adjustment cable force and the method of applying cable force,which avoids the problem of inconvergence caused by the influence of initial cable force inthe traditional influence matrix method.In addition,according to different situations of cableforce optimization in practical applications,the displacement constraint conditions in thedouble matrix method can be extended to the main tower bending moment,main girderbending moment,section stress and other constraints,which is convenient for application inthe design of long-span suspension bridges.3 tabs,6 figs,28 refs.