A 3D absolute nodal coordinate finite element model to compute the initial configuration of a railway catenary

•A 3D finite element model of the railway catenary using ANCF is defined.•The method considers the constraints imposed during stringing of the catenary.•Two methods proposed: pointwise height constraint and distributed optimization.•The methods were applied to real catenaries with straight and curved paths. In this paper we propose a method of finding the initial equilibrium configuration of cable structures discretized by finite elements applied to the shape-finding of the railway overhead system. Absolute nodal coordinate formulation finite elements, which allow for axial and bending deformation, are used for the contact and messenger wires. The other parts of the overhead system are discretized with non-linear bars or equivalent springs. The proposed method considers the constraints introduced during the assembly of the catenary, such as the position of droppers, cable tension, and height of the contact wire. The formulation is general and can be applied to different catenary configurations or transitions both in 2D and 3D with straight or curved track paths. A comparison of the results obtained for reference catenaries in the bibliography is also included.