函数传递法求解悬链线问题

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.