函数传递法求解悬链线问题

悬链线问题是一类经典又多变的力学问题，其曲线构形指导着桥梁等工程应用的结构设计。为了求得结构特征或载荷特征不同的悬链线的变形，提出了一种基于传递矩阵法思想的、通用性较好的求解方法。首先，提炼出悬链力学模型，将悬链顺序划分成若干简单单元，结合单元力平衡和本构-几何关系解得单元特征函数方程组，顺序嵌套单元特征函数方程组获得整体特征函数方程组；然后，使用离散Newton迭代法对该非线性方程组进行求解，获得悬链的受力和变形；最后，算例验证了结果与解析解的一致性。函数传递法对具有复杂结构特征和载荷特征的悬链线问题有很好的适用性，对求解其他可划分为若干首尾相接结构单元的结构系统的广义变形也适用。 

Solving catenary problem using function transfer method

Catenary problem is a kind of classical and changeable mechanical problem, whose curve configuration guides the structural design of engineering applications such as bridge. In order to obtain the deformation of catenary with different structural or load characteristics, a general method based on transfer matrix method is proposed. The catenary mechanics model is extracted, and the catenary is divided sequentially into several simple elements. The characteristic function group of element state parameters is obtained by combining element force balance and constitutive-geometry relationship. The whole characteristic function group is obtained by nesting element characteristic function group sequentially. Then the discrete Newton iterative method is used to solve the equations of nonlinear whole characteristic function group, and finally the forces and deformation of catenary are obtained. An example showed that the results were consistent with the analytical solution. The function transfer method is applicable to the catenary problems with complex structural characteristics and load characteristics, and also applicable to solving the generalized deformation of other structural systems which can be divided into several head-to-tail structural elements.