基于角平分线的工程滑移索结构分析方法

Analytical Method for Sliding Cable Structures in Engineering Based on Angle Bisector

针对滑移索结构,提出了一种基于滑轮相邻索单元角平分线的简捷分析方法,解决了其内力和变形求解复杂的难题.具体算法如下:(1)采用固定铰模拟滑轮对索的约束作用,利用无应力长度调整影响矩阵求解角平分线垂直方向约束反力为零时,各子索无应力长度调整量;(2)根据调整后子索线形计算新角平分线的方向角,按照步骤(1)重新计算,重复至索线形(包括角平分线方向角)和内力收敛.基于此算法编制分析程序,通过2~4次迭代即可得到高精度的收敛解,实现滑轮处索力连续性和滑移索总无应力长度恒定的目标.计算示例和工程实例证明了此算法的正确性和高效性.

In this paper, a simplified analysis method is proposed based on angle bisector to effectively get the internal forces and deformations of the sliding cable structure. First, the cable constraint caused by the pulley is modeled by fixed hinge. The stress-free length adjustment, internal forces, and alignment of sub-cables are obtained by using the unstressed length adjustment matrix constrained by the reaction forces vertical to the angle bisector direction equaling zero. Next, the angle of bisector is modified according to the deformed structure. The first step will be iterated until the cable forces are equal within tolerance. An analysis package is programmed based on this and numerical results show that the tension continuity and deformation relationship could be achieved by 2 to 4 iterations with high precision. The numerical example and engineering example demonstrate the correctness and efficiency of the proposed method.