埃特金加速迭代法及其在单跨悬索状态方程中的应用

摘要

针对悬索斜抛物线状态方程,引入埃特金加速迭代解法,阐述其基本原理和计算步骤.结合工程索道案例,通过比较分析普通迭代法、牛顿迭代法和埃特金加速迭代法的求解过程,得到不同温度下无荷的悬索跨中张力、索长、中央挠度及中挠系数的变化规律,以及温度效应对悬索参数的响应规律,结果表明埃特金加速迭代法实用且简便.%For the inclined parabolic state equation of flexible cable,Aitken rapid iteration algorithm was introduced,and the basic principle and calculation steps were also presented.Taking engineering cableway as an example,the solving processes of common iteration method,Newton iteration method and Aitken rapid iteration algorithm were analyzed and compared,the variation rules of span tension,cable length,central deflection and central deflection coefficient of unloading flexible cable under different temperatures were obtained,and the response pattern of flexible cable parameters to temperatures was also got,the result showed Aitken rapid iteration algorithm had practicality and simplicity.