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

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.