Multiscale Modeling of Transition Section with Continuously Welded Rail Based on Homogenization Method

To analyse the stress distribution of continuously welded rails at transition sections under the effect of temperature, a multiscale model of the transition section with two-terminal rail lines is proposed. Owing to the structural regularity of the two-terminal bridge and the subgrade extending from the transition section, a simplified macro-scale line model is built based on the macro-equivalent properties of a typical structural unit, which can be evaluated by the asymptotic homogenisation method. As for the transition section, a minor-scale model is built to involve the key details. These sub-models of different scales are connected to each other based on the interface consistency conditions. The homogenised model of the two-terminal extension segments provides a useful boundary condition for the central transition section in the process of solving the multiscale model. Further, the solutions of different-scale models are obtained by model decomposition, which avoids high-dimension matrix operations for the single-scale model. The simulation results show that the multiscale model with the asymptotic homogenisation method has fewer computations than the traditional finite model, which consequently has a faster calculating speed. Comparing the simulation results of the termination cutting off and abutments with measurements from the Xinbianhe bridge of the Beijing–Shanghai high speed railway, the average correlation is approximately 0.8, and the varying trend of simulation results is consistent with the measured data.