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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。
Based on the basic theory of elasticity, the stiffness matrix method is used to derive the numerical solution of the statics of the three-dimensional multilayered elastic layered system used in Cartesian coordinates. The introduction of two-dimensional Fourier transform and Gaussian integration method, based on MATLAB mathematical software platform for the preparation of computational procedures to achieve three-dimensional multilayer elastic layered theoretical calculation method of numerical solution. Aiming at the typical ballastless track under-rail structure, the proposed method and the corresponding calculation program were used to conduct the static analysis, and the calculated results were compared with those obtained by using the general finite element program ABAQUS. The results show that the maximum vertical displacements of the foundations under ballast orbit are respectively 1.50 and 1.95 mm and the maximum vertical stresses are 0.34 and 0.21 MPa, respectively, using the proposed method and the common finite element method. The calculated results are close to the calculated values The laws of component transformations reflected by each state are basically the same. The proposed calculation method and its corresponding calculation program can be applied to the statics calculation of multilayered elastic layered systems.