An adaptive variable-length cable element method for form-finding analysis of railway catenaries in an absolute nodal coordinate formulation

High-speed trains collect electric current from a railway catenary composed of metal cables. The current collection quality is affected by the geometric shape of the catenary. As catenary cables have large initial displacements and can exhibit strong vibration and undergo large deformations in train operation, a new method based on the cable element with an adaptive variable length in the absolute nodal coordinate formulation (ANCF) is proposed to accurately compute the initial equilibrium configuration of the catenary. The proposed method relies mainly on an installation simulation of a catenary structure with variable-length ANCF cable elements. The length variations of these elements are correlated with the assembly conditions of the structure. The governing motion equations of the variable-length cable elements are derived. In the proposed method, a railway catenary in a simple configuration is modeled with variable-length and constant-length cable elements that have initially straight shapes and are strain-free. By adjusting the element lengths, the structure is tensioned to reach the desired equivalence state. The proposed method essentially changes the structure from an arbitrary configuration to a constrained configuration using a dynamic simulation. The proposed method is insensitive to initial conditions and is easily implemented with complex railway catenaries. The validity and accuracy of the method were demonstrated by comparing the obtained results with results reported in the literature. •A form-finding method of railway catenaries is proposed based on the absolute nodal coordinate formulation (ANCF).•The method computes the catenary configuration by simulation with ANCF cable elements of adaptive variable length.•The length change of cable element is correlated with assembly conditions of the catenary.•The results of illustrative example solutions show the excellent performance of the proposed method.