基于均匀化方法的无缝线路过渡段多尺度建模

为分析无缝线路过渡段的钢轨应力分布问题，提出了针对路桥过渡段及周围延伸线路的多尺度建模方法. 针对过渡段两端的桥梁和路基所具有的周期性延伸的特点，采用渐进均匀化方法计算周期性结构的宏观等效性能，建立过渡段周围区段的宏观尺度模型. 对于过渡段内部，则采用小尺度建立包含关键细节的局部精细化模型. 不同尺度的局部模型之间按变形状态一致的原则建立边界耦合条件，构成完整的长线路模型. 两端线路的宏观均匀化模型为过渡段的局部状态分析提供完整的边界条件，同时通过对整体线路分层求解，避免了常规有限元模型的高维矩阵运算. 仿真试验表明:采用均匀化方法的多尺度模型比传统有限元模型的计算规模更小，因此求解速度更快；模型结果与京沪高速铁路宿州东站新汴河大桥过渡段的现场实测结果变化趋势一致，在主端刺、桥台支座处的轨道变形与实测数据的相关系数达到0.8. 

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.