This paper presents a nonlinear finite element formulation for modeling the structural flexibility in multibody railroad vehicle systems. The formulation presented in this paper allows for modeling the structural flexibilities of the pantograph/catenary system, car body, and the track structure as well as their coupling with the dynamics of other components of high speed rail systems. The main outcome of this study is the development of a procedure that allows building a complex track or car body models that include significant details using a finite element preprocessor computer program. For example, the proposed method allows for developing at a preprocessing stage a track model that includes significant details and accounts for the effects of ties, fasteners, ballast, etc. The detailed track or car body model is used as an input to the general purpose flexible multibody computer program for a nonlinear analysis that accounts for the dynamic coupling between the track and car body flexibility and the vehicle coordinates. In order to achieve this goal, two different types of interpolations are used in the kinematic equations developed in this study; the geometry interpolation and the deformation interpolation. In the proposed formulations, the rails can have arbitrary geometry which is described using the isoparametric geometric interpolation. The coordinates of the polynomials used in this interpolation represent constant position and gradients coordinates, which are used to describe accurately the rail geometry. On the other hand, the rail deflections as well as car body deformations are described using the deformation interpolation and the nonlinear finite element floating frame of reference formulation. In the formulation proposed in this paper, the rail tangent and normal vectors as well as other geometric parameters such as the curvature and torsion at the wheel/rail contact points are expressed in terms of the rail deformation coordinates. The nonlinear dynamic coupling between the rail geometry and the vehicle dynamics is also considered in the formulation proposed in this paper. In particular, the longitudinal, lateral and spin creepages are expressed in terms of the track displacements which are the result of the wheel/rail contact forces. This nonlinear coupled analysis allows for more accurate prediction of the railroad vehicle dynamics. This paper also proposes a new efficient finite segment method based on the concept of rigid finite element to model track structure. Numerical results are presented in order to demonstrate the use of the formulation proposed in this study.

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