A simple and efficient numerical model for dynamic interaction of high speed train and railway structure including derailment during an earthquake

A simple and efficient numerical model to solve the dynamic interaction of a high-speed train and railway structure including derailment and post-derailment during an earthquake is given. Mechanical model to express contact-impact behaviours between wheel and rail before derailment and between wheel and track structure after derailment is discussed. A contact model based on multipoint contact springs on the contact surface between wheel and the track structure after derailment is given. An efficient contact element to express contact-impact behaviour between the car body of the train and the railway structure during and after derailment is also given where the contact stiffness is described as a nonlinear function of the contact displacement. The motion of the train with nonlinear springs and dampers is modelled in multibody dynamics. The railway structure is modelled with various finite elements. The modal reduction is applied to equations of motion of the train and railway structure. A robust time integration using the exact time integration has been developed in the modal coordinate to solve the radical dynamic interaction including derailment during an earthquake to avoid the round-off error which normally appears in the numerical time integration for very small time increments. Numerical example is demonstrated.