Research Of Finite Element Method For The Problem Of Elastic Wave In Two-dimensional Inhomogeneous Anisotropic Medium

Most of the media in nature are inhomogeneous and anisotropic. Numerical method is the primary method to solve problems of heterogeneous anisotropic media. The simulations of seismic wave field play a very important role in oil exploration, the design of the structure ofhouses, earthquake resistance and disaster reduction. At present,numerical methods and analytical methods are both major methods to solve seismic wave equation problems.Numerical method is mainly used to solve the complex geological model.Many numerical methods are used to solve seismic wave equation problems, such as fourier pseudo dissemination and reflectivity method, finite difference method, finite element method, etc. Each method has its own advantages and disadvantages. Finite element method is used in this article to simulate and solve elastic wave equation problems. The main advantage of the finite element method is that it can let the simulation of any actual terrain and geology well solved. Different boundary conditions should be set according to actual terrains. The model should be divided into triangular or quadrilateral to make goodapproximation to the actual terrains to meet the authenticity of the simulation of complex terrains. The traditional finite element method (FEM) has the following disadvantages: the high requirement of the performance of the computer, especially the memory and the computation speed of the computer and the large amount of calculation. Aiming at these shortcomings, the high order isoparametric element and dividing unit matrix is adopted to improve the computational efficiency.The main content of this paper :(1) Heterogeneous anisotropic elastic wave equation is set by variation method based on the elastic dynamics theory. Then the heterogeneous anisotropic elastic wave equation of finite element form is derived. Then the corresponding element stiffness matrix and elementmass matrix, damping matrix unit of general form are derived.(2) Quadrilateral isoparametric element and bilinear interpolation function is used to derive the heterogeneous anisotropic elastic wave equation of finite element form. The parameters of the isoparametric element material are given, making the calculation model similar to the actual model, meeting the demand of engineering calculation, improving the calculation speed.(3)The condition of the stability which meets the parameters of the finite element method to solve wave equation is given.(4) MATLAB is used to write programs, giving the corresponding numerical example of a heterogeneous anisotropic medium and doing analysis with analytical solution to verify the validity of the program of this paper. Isoparametric interpolation function processing of the parameters of the material is used to improve the precision of calculation. Besides, the programs not only meet the accuracy requirements but have the advantages of high speed calculation and low requirement of the memory of the computer as well.