Generalised electromagnetic forces in an absolute nodal coordinate formulation

Abstract

This paper focuses on the mechanical, dynamic numerical modelling of an electrical-current-carrying cable using a non-linear absolute nodal coordinate formulation. The derived equations are an expansion of the mechanical equation of motion. They allow interdisciplinary mechanical and electrical research of the cable dynamics where large electrical currents are present in the cables. A vector of the generalised electromagnetic forces in the absolute nodal coordinate formulation for a current-carrying finite element of arbitrary length is derived. For the cable elements a filament approach is used to determine the magnetic flux density. To round off the method’s applicability, the contact forces that can occur between free-moving cables are also considered. The generalised electromagnetic forces are derived and expressed with the pre-computed matrices. As the numerical testing shows, the presented method is computationally very effective. The equations are general and can be applied to any similar dynamic systems.