采用刚度矩阵法的弹性层状体系数值解法

Numerical method of multi-layer elastic system by using stiffness matrix method

从弹性力学基础理论出发,采用刚度矩阵法,推导了应用于直角坐标系下的三维多层弹性层状体系静力学数值解法。引入二维傅里叶变换及高斯积分求解法,基于MATLAB数学软件平台编制计算程序,实现三维多层弹性层状体系理论计算方法的数值求解。针对典型有砟轨道轨下基础结构,采用提出的计算方法和编制的相应计算程序对其进行静力学分析,并将所获得的计算结果与采用通用有限元程序ABAQUS的计算结果进行对比。分析结果表明:采用提出的计算方法和通用有限元计算方法获得有砟轨道轨下基础最大竖向位移分别为1.50、1.95 mm,最大竖向应力分别为0.34、0.21 MPa,计算结果较为接近,计算反映出来的各状态分量变换规律基本一致,提出的计算方法及其相应计算程序可应用于多层弹性层状体系的静力学计算。

By using the theory of elastic mechanics and stiffness matrix method,a numerical method of static mechanics for calculating 3D multi-layer elastic system under rectangular coordinate system was developed.2D Fourier transform and Gauss integral method were used,a calculation program was given based on MATLAB mathematical software platform,and the numerical solution of 3D multi-layer elastic system was got.The static mechanics analysis of ballast track foundation structure was carried out by using the numerical method and program,and the calculation results were compared with the results obtained by using general finite element program ABAQUS.Analysis result shows that the maximum vertical displacements of ballast track foundation are 1.50,1.95 mm respectively by using the numerical method and general finite element calculation method,and the maximum vertical stresses of the foundation are 0.34,0.21 MPa respectively by using the two methods.The calculation results are close to each other,and the conversion rules of state components are basically the same according to the calculation,so the proposed numerical method and program can be applied to the static mechanics calculation of multi-layer elastic system.2 tabs,9 figs,24 refs.