整体桥上无缝线路钢轨非线性附加力算法研究

Research on nonlinear additional force algorithm of continuously welded rails on integral bridges

在计算桥上无缝线路的纵向阻力时,阻力模型通常采用无缝线路设计规范中建议的双折线纵向阻力模型,即有载与无载分别考虑后再线性叠加,未考虑钢轨的非线性行为。在计算方法上,工程中常采用有限元模型进行计算,有限元法建模效率较低、不便于对各设计参数的更改。为准确快速求得高速铁路整体式桥上梁轨相互作用下的钢轨附加力、钢轨位移、钢轨弹塑性分界点及整体桥墩顶位移等参数值的大小,提出更贴近于桥上钢轨实际受力的多折线纵向阻力模型,并采用建立微分方程组的数值解法,通过建立具有变化规律的平衡矩阵式来求解桥上无缝线路钢轨纵向阻力值的相关参数。研究分别给出了有载、无载工况下求解整体式桥上钢轨附加应力值的规律性矩阵式,经有限元法验证,得到该方法下的温度、制动力附加应力值的误差均较小,分别为1.6%和0.5%。并结合规律矩阵式得到同时考虑有载与无载下的非线性附加力的计算方法,非线性叠加与线性叠加两方法下的总附加应力计算差值随着制动/牵引力下的梁轨相对位移值的增大而增大,当梁轨相对位移小于1.8 mm时,2种方法误差少于5%,可忽略不计,但随着梁轨相对位移的进一步增加,非线性阻力模型计算的结果则更贴近于实际。

In calculating the longitudinal resistance of the continuous welded rails on the bridge,existing models typically use the two-fold line resistance model and linear superposition proposed in the Code for Design of Railway Continuous Welded Rails.They barely consider the non-linear behavior of rails.In terms of the calculation methods,the finite element method(FEM)models are often used in engineering applications,which however are time-consuming.It is also not easy to attempt different combinations of design parameters in such FEM models.To obtain the additional force and displacement responses of the high-speed rail accurately and efficiently,the elastoplastic boundary point and overall pier-top displacement,the longitudinal resistance model of the multi-fold line closer to the actual stress on the bridge were proposed.The numerical solution was used to establish differential equations.The correlation parameters of the longitudinal resistance were solved by establishing a variational balance matrix.The regular matrix formulas of the longitudinal additional stress terms on an integral bridge under loaded and unloaded conditions were given.The finite element method was verified.The error of temperature and additional braking force stress under this method are small,which are 1.6%and 0.5%respectively.The calculation method of nonlinear additional force was obtained by combining the matrices corresponding to loaded and unloaded conditions.The difference of the additional stress between two modeling conditions increases with increasing braking/traction.When the relative displacement of beam and rail is less than 1.8 mm,the error of the two methods is less than 5%and thus can be ignored.However,with the further increase in the relative displacement,the results calculated by the nonlinear resistance model are closer to the real measurements.