An alternative simple multibody system approach for modelling rail flexibility in railroad vehicle dynamics

Abstract In a previous investigation, a non-linear finite element formulation for modelling rail structural flexibility in multibody railroad vehicle systems was presented. This formulation required the use of isoparametric interpolation based on the finite element absolute nodal coordinate formulation (ANCF) in order to have a consistent interpolation for the geometry in the current deformed configuration. That is, the same interpolation functions used for the geometry description in the undeformed reference state are also used for predicting the geometry in the current deformed state. This approach, however, becomes less attractive when a degree of derivative continuity higher than the one provided by ANCF elements is required. In this investigation, an alternate simpler approach is proposed for modelling rail and track flexibility. The proposed new method, which is based on the floating frame of reference formulation, allows for general modelling of rail and track flexibility, can be used to impose a higher degree of continuity on the derivatives at the nodes that define the rail geometry in the reference configuration, and can be used to systematically couple finite element computer programs with flexible multibody system codes, allowing for the development of detailed track models that include rail, tie, and fastener flexibility as well as soil characteristics. In the proposed method, track geometry is defined in a preprocessor computer program using nodal points. In addition to the location of the nodes and Euler angles that define the orientation of the profile frame at the nodes, first, second, and third derivatives of the locations and Euler angles are defined by the preprocessor computer program. Numerical examples are presented in order to demonstrate the effect of track deformation in railroad applications.