弹性悬链线方程在柔性光伏支架悬索计算中的应用

Application of Elastic Catenary Equation in the Calculation of Suspension Cable of Flexible Photovoltaic Support

柔性光伏支架采用了小矢跨比(小于1/30)的悬索结构,索的弹性伸长使结构表现出很强的几何非线性。本文通过选取合理的参数,给出了弹性悬链线参数方程的简单形式,并分析了弹性悬链线方程的性质;在给定悬索两端点相对位置和悬索无应力长度条件下,推导了悬索端部索力求解的迭代方程及迭代初值选定方法;最后,通过工程实例介绍了本文方法在柔性光伏支架悬索计算中的应用,并验证了该方法的收敛性。本文计算方法可在Excel中输入公式进行计算,经过3~4次迭代即可收敛,可为柔性光伏支架等悬索的静力分析和结构设计提供参考。

The suspension cable structure with small rise-span ratio(less than 1/30)is adopted in the flexible photovoltaic support,and it has strong geometric nonlinearity because of the elastic elongation of the cable.Choosing a reasonable parameter,the simple form of elastic catenary equation was given,and the properties of elastic catenary equation were analyzed.Based on the relative positions of the two ends and the stress-free length of the cable,the iterative equation of the end force of suspension cable was derived,and the method to select the initial values of the iterative method was given.The calculation process of the proposed method was introduced by an engineering example of the flexible photovoltaic support cable,and the convergence of the iterative method was verified.The method in the paper can be calculated by inputting formulas in Excel,the convergence can be achieved after 3~4 iterations,which can provide a reference for static analysis and structural design of the suspension cable such as flexible photovoltaic supports.