Enhancement of the finite-element method for the analysis of vertical train—track interactions

Abstract

The accuracy of the simulation of train-track interaction can be improved by adding a node at the point of loading, when a contact force exists within the beam element that models the rail. This causes difficulties in the formulation and entails large computational times since the node moves along with the point of contact. In this study, a more simplified method that can represent the discontinuities of slope deflection at the location of both the sleeper and of the moving contact force, while employing the customary finite-element method, has been presented. The simulation of the existence of such an added node without explicitly including it is realized by modifying the Hertzian spring coefficient and adding the additional mass matrix to the existing mass matrix. Also, to enhance the convergence and to overcome the computational burden of load vector calculations at all iterations, a modified Newmark-β integral scheme is proposed. The suggested model was validated by comparing the results with field-test data and other numerical models reported in the literature by other researchers.

Implementation of Timoshenko element local deflection for vertical track modelling

“…In the first group, those models that account for the track as an in-plane system describing only the vertical motion of half-track, and in a second group, those models that account for the coupling between the rail through the sleepers, and therefore, describing in some extent the whole track. 2-dimensional (in-plane) models are commonly used [9][10][11][12][13][14][15], since, in pursuit of simplicity and clarity, they allow assessing new approaches. For instances, Refs.…”

“…The non-physical response of the Timoshenko element has been previously tackled by Yang [11] and Koro et al [9]. The model proposed by Yang [11] uses conventional Timoshenko element and the formulation of a moving node in order to define an equivalent contact stiffness. This approach provides significant enhancement, but the slope discontinuity is not fully removed.…”

“…In spite of obtaining good results, the method forces to restructure the stiffness and mass matrices at each time step and the number of DOF is significantly increased. Both alternatives present drawbacks, whether the discontinuity is still noticeable [11] or the formulation of the problem slows down temporal simulations [9].…”

“…Secondly, the prediction of contact forces due to short-pitch corrugation is significantly enhanced when compared to conventional Timoshenko element formulation. The validation of the methodology is done with respect to previous studies that make use of in-plane track models and that account for the wheel as a simple mass attached to the rail by a Hertzian spring [10,11].…”

Comparison of dynamic effects of high-speed traffic load on ballasted track using a simplified two-dimensional and full three-dimensional model

“…An important number of research works on this subject have contributed to relevant technical advances. Some studies [4][5][6][7][8][9][10][11][12] have proposed two-dimensional (2D) interaction models in which the vehicle is modelled as one bogie or more realistic models based on rigid bodies connected by suspension systems, and modelling the track as discrete support model. Other detailed models [13][14][15][16][17][18][19] were developed to investigate the vertical and lateral dynamic responses of the vehicle-track coupled system in which the vehicle is treated in a more realistic way, and the track is modelled as the three-dimensional (3D) discrete support model or 3D finite-element model.…”