悬索桥索鞍预偏量的牛顿-拉斐森算法

Newton-Raphson Algorithm for Pre-offsetting of Cable Saddle on Suspension Bridge

为了在悬索桥索鞍预偏量的影响矩阵中计入预偏量初值的影响,且考虑索鞍切点变化、索鞍顶非悬链线区段对主缆无应力长度的修正及主缆与索鞍间摩擦力的影响,提出索鞍预偏量的牛顿-拉斐森算法。根据索鞍平衡关系及相邻跨主缆线形基本方程,推导出索鞍及主缆的11个状态方程,能完全确定11个独立的未知量,采用牛顿-拉斐森算法建立预偏量的雅克比影响矩阵,推导出矩阵中各元素的表达式,给出了初值的取值范围及约束条件,保证了计算的收敛性;并与1/30缩尺比全桥模型试验进行对比分析以验证算法的可靠性。结果表明:试验值与所提出算法的计算值吻合较好,验证了该方法的可靠性。

To consider the influence of initial pre-offsetting in the influence matrix of cable saddle of pre-offsetting on suspension bridge,as well as the influences of structural parameters（i.e.,the movement of tangent point at cable saddle,the correction of the unstressed cable length on the non-catenary segments at the top of cable saddle,the frictions between cable and saddle）,Newton-Raphson algorithm was proposed to calculate the pre-offsetting of cable saddle.According to the equilibrium relationship of cable saddle and the fundamental equations of adjacent across main cable shape,11 state equations of cable saddle and cable were deduced to solve the 11 independent unknown quantities.Then the Newton-Raphson algorithm was adopted to establish the Jacobian influence matrix of pre-offsetting,and the expressions of each element in the matrix were derived.Furthermore,the range and the constraint conditions of initial value were given to ensure the convergence of the calculation.The comparative analysis was conducted with a 1/30-scale bridge model test to verify the reliability of algorithm.The results show that calculated values are in good agreement with the test results by the proposed algorithm,which indicates the reliability of the numerical method.