The Finite Element Method For The Wave Motion Problem In Inhomogeneous Elastic Media With Interface

Heterogeneous medium widely exists in our production life. With the development of material technology and geological exploration technology. The forefront of research have been made by homogeneous medium transition to heterogeneous medium. The problem of interface also widely exists in the study of the inhomogeneous medium. The research of interface-wave interaction has caught the attention of the scholars widely. Due to the heterogeneous medium containing interface fluctuation problem research can be well applied to the study of and nondestructive testing engineering and other fields. So the research on it has very important theoretical significance and practical application value.In this paper , basing on the theory of elastic wave , I firstly use coordinate related functions to describe the inhomogeneity of the medium,then derive by variational methods used for heterogeneous medium wave problem analysis of finite element method,Secondly,I describe the interface, give the concept of interface finite element method. And I have deduced corresponding stiffness matrix and damping matrix interface unit based on the finite element method. The main work of this paper is as follows:1.Introducing the definition of mechanical model of the interface and the classification of interface , making the interface to fully combined interface , stripping interface and contact interface, then describing the boundary condition of each interface.2. Describing the inhomogeneous medium , and pushing the general form of the inhomogeneous medium finite element method (FEM) from the method based on variational methods, then introducing a kind of improving the efficiency of heterogeneous medium finite element calculation of material parameters such as ginseng interpolation method.3. Describing the interface to the finite element model , giving the definition of the interface unit,establishing the triangle unit with rectangular element,and their stiffness matrix and damping matrix is given.4. Using heterogeneous medium containing interface unit fluctuation problem of finite element program for the MATLAB calculation and analysis on the problem of plane SH-wave incident , and comparing the different positions interface for the corresponding observation points of the effect of displacement amplitude and its potential engineering application.5. Using heterogeneous medium containing interface unit fluctuation problem of finite element MATLAB for incident plane P-wave problem for calculation and analysis, and comparing the different location interface for the corresponding observation points of the effect of displacement amplitude and its potential engineering application.