Numerical Substructure Method For Vehicle-track-bridge Vertical Coupling System Of High-speed Railway

The vehicle-track-bridge coupling system of high-speed railway is a large-scale nonlinear dynamic system.The degree of freedom for the fine vehicle-track-bridge coupling system is usually large.The high frequency contact of the wheel and rail requires short time steps.The finite element matrix of the system will take up a lot of memory and the calculation will be time-consuming.It is necessary to develop a new modeling method that can take into account accuracy and efficiency.This paper presents a novel two dimensional(2D)wheel-rail interaction(WRI)element for simulating the vertical wheel-rail interaction and implements the element in a finite element(FE)framework OpenSees.This element consists of a wheel node and the nodes of the beam elements with which the wheel may interact.The WRI force was calculated by solving a cubic polynomial equation.This force was then used to obtain the internal force of the WRI element.The coupling element was verified by using existing examples in the literature,and then used to analyze the dynamic responses of a high speed train passing through a rail with irregularity and subject to an earthquake.This novel element is easy to integrate into a general FE software platform.Together with FE models of vehicle,track and bridge,the general model that is used to solve by newton-raphson(NR)method is built.The coupling element is able to be used in nonlinear dynamic analysis of vehicle-track-bridge systems with complexity,e.g.,considering rail irregularity,wheel-rail separation and earthquake.Based on numerical substructure method(NSM),this paper presents an efficient calculation method for vehicle-track-bridge vertical coupling system of high-speed railway that can take into account the accuracy and efficiency.The integration area is divided by different scales element,and the vehicle-track-bridge vertical coupling system is separated into main structure and substructure.The main structure is discrete in larger elements to simulate bridges.The fine substructure is discrete in smaller elements,taking into account the vehicle-track-bridge coupling interaction.Through Client-Server(C\S)software technique,Newton algorithm between main structure and substructure is implement and the numerical substructure method(NSM)for vehicle-track-bridge vertical coupling system of high-speed railway is established.Compared with the results of the conventional method,the accuracy and efficiency of the numerical substructure method applied to vehicle-track-bridge vertical coupling system of high-speed railway are verified.In order to make the Numerical substructure method more convenient and avoid modifying the nodes and elements of the model,a ' ring' substructure is introduced.The WRI element is used to model the fine 'ring' substructure.The substructure boundary dynamic response is obtained by shape function interpolation of the main structure dynamic response.The numerical substructure method(NSM)for vehicle-track-bridge vertical coupling system can be used to the case of train keeping driving.Through the use of isolation zones of different lengths,the effect of isolation zone length on the calculation accuracy and efficiency of the NSM model was studied.This paper evaluated the accuracy and efficiency of the numerical substructure method for vehicle-track-bridge vertical coupled system under irregularity,earthquake or smooth track and no earthquake.The research shows that the numerical substructure method can reduce the degree of freedom of the system and improve the computational efficiency.The NSM method provides a ideal modeling method for vehicle-track-bridge vertical coupling system of high-speed railway.It can balance both accuracy and efficiency and has potential engineering application capabilities.