铁路轨道强度及弹性点支承连续梁的Spline函数解法

SPLINE FUNCTION SOLUTION TO THE PROBLEM OF RAILWAY TRACK STRENGTH AND CONTINUOUS BEAM ON ELASTIC POINT SUPPORTS

本文从集中荷载作用下铁路轨道的钢轨及弹性点支承连续梁的挠曲曲线是三次Spline曲线出发,利用Spline函数和工程力学基本知识,建立了挠曲曲线位移及二阶导数列向量满足的联立矩阵方程,从而可以解得钢轨位移、弯矩及剪力,同时,自然地给出挠曲曲线的表达式。与有限单元方法比较,本文方法具有公式推导简捷,思路清晰,便于计算机计算,而且计算工作量较小等优点。

On the basis that the deflection curves of track rails and continuous beam on elastic point supports are cubic curves, we establish the simultaneous matrix equation satisfied by the deflection and differential quotient of second order of the deflection curve, using the knowledge of spline function and engineering mechanics. Thereby we can solve the deflection, moment and share of the rail. At the same time, the deflection curve is obtained naturally. Compared with the finite element method, the method put forward in this paper has the following merits: derivation of the formula is forthright; the train of thought is clear it is easily adapted for computation on computer and the amount of computation is comparatively small.