Spatial finite element formulation for the pantograph/catenary systems

This paper describes a three-dimensional large deformation finite element formulation for the analysis of the multibody pantograph/catenary systems. The large deformation of the catenary is modeled using the three-dimensional finite element absolute nodal coordinate formulation. A non-generalized arc-length parameter is introduced in order to be able to formulate the joint between the catenary and pan-head and to accurately predict the location of the contact point. The resulting system of differential and algebraic equations formulated in terms of reference coordinates, finite element absolute nodal coordinates, and non-generalized arc-length and contact surface parameters are solved using computational multibody system algorithms. A method is also proposed to deal with the problem of the loss of contact between the pan-head and the catenary cable.