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

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.