基于分段悬链线理论的悬索分析矩阵迭代法

The matrix iteration method for analysis of suspension cable based on segmental catenary theory

通过分析现有悬索计算的主要方法,在分段悬链线解析计算方法的基础上,结合求解非线性方程组的牛顿迭代法,提出了适用于悬索分析的矩阵迭代方法.根据解析推导给出了悬索矩阵迭代法的切线刚度矩阵构造方法,分析了刚度矩阵的特点,针对特定的工程问题列出了悬索找形的迭代计算流程.该方法计算量小,效率高,计算精度能够满足实际工程需要.通过与其他文献的数值计算结果进行对比,验证了所研究方法的可靠性.该方法适用于悬索桥、货运索道等各类悬索结构的分析计算.

A matrix iteration method is proposed based on the analytic method of segmental catenary for the suspension cable. The method was developed from the Newton iteration method for the nonlinear equations according to the analysis of different common methods. The tangent stiffness matrix of the iteration method was presented and the characteristics of the stiffness matrix were discussed. Then the iterative calculation process of suspension cable＇s form finding for the specific engineering problem was listed. The method offers significant improvements on accuracy, efficiency and calculation amount of the solution, which can meet the needs of practical engineer- ing. The results of the Newton iteration method are compared with the numerical results in other literatures and the contrast verifies the reliability of this method. The method is suitable for the analysis of suspension bridges, cargo ropeways and other various types of cable structures.