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A novel practical element is presented for simulating the vertical wheel-rail interaction (WRI) of vehicle-track-bridge (VTB) coupling systems. The WRI is time- and location-varying, which makes the simulation of the VTB system complicated. The new element simulates the WRI using a location dependent internal resisting force, which enables the finite element (FE) model of the VTB system to remain unchanged in analysis. This element is capable of simulating the nonlinear WRI, the rail irregularity and the ‘additional’ displacement of the rail. The ‘additional’ displacement is the extra displacement caused by the WRI besides that interpolated from the element nodal displacements, which is usually ignored by existing models, but may be non-negligible in some cases. The WRI element is implemented into a general FE software framework, OpenSees, and verified by the dynamic analysis of a simply-supported beam subjected to a moving sprung mass. Furthermore, a realistic VTB system with a moving four-wheel vehicle is investigated to evaluate the cases where the additional displacement and nonlinear WRI should be considered. Finally, using another realistic VTB system subjected to rail irregularities and earthquakes, the effects of rail irregularity and earthquake on the dynamic responses of the WRI system are studied and compared.

Consistent tangent stiffness plays a crucial role in delivering a quadratic rate of convergence when using Newton’s method in solving nonlinear equations of motion. In this paper, consistent tangent stiffness is derived for a three-dimensional (3D) wheel–rail interaction element (WRI element for short) originally developed by the authors and co-workers. The algorithm has been implemented in finite element (FE) software framework (OpenSees in this paper) and proven to be effective. Application examples of wheelset and light rail vehicle are provided to validate the consistent tangent stiffness. The quadratic convergence rate is verified. The speeds of calculation are compared between the use of consistent tangent stiffness and the tangent by perturbation method. The results demonstrate the improved computational efficiency of WRI element when consistent tangent stiffness is used.

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This paper presents a modified numerical substructure method for simulating the dynamic response of vehicle–track–bridge (VTB) systems. The method can be used to analyze large-scale VTB systems accurately and efficiently. Based on the principle of virtual work, the equations of motion are derived for two separate subsystems, i.e. a small-scale of finely modeled VTB substructure and a coarsely meshed large main bridge subsystem using different level of refinement. Different from the conventional dynamic substructuring approaches, the bridge spans close to the vehicle are modeled in both the main and substructure models, and the contradiction of repeatedly modeling is solved using a “nonlinear force corrector”. A special wheel–rail interaction (WRI) element is used to simulate the fast-moving interaction force between the vehicle and rail. In this way, the two models remain unchanged while the vehicle moves forward, and the computational accuracy is the same as the large-scale purely refined model, while the efficiency is significantly improved, particularly, for the large-scale long VTB systems. Two examples of realistic VTB systems with either smooth or un-smooth rails are used to verify the proposed method. The results demonstrate that the presented method has remarkable advantages of computational efficiency and accuracy, providing a practically useful tool for analysis of large-scale VTB systems.