Abstract
This paper focuses on the explicit dynamic analysis of wave propagation in heterogeneous materials using the extended finite element method (X-FEM). Since the enriched approximation in the X-FEM enables us to introduce the material discontinuities independently of finite element mesh, mesh-free and image-based analyses of heterogeneous materials can be realized. To apply the X-FEM to wave propagation analyses, we discuss the lumping techniques of mass matrix in enriched elements, and show that the mass matrix components in enriched elements does not tend to zero even if the material interface reaches the boundaries of enriched elements. In this paper, Chapter 2 shows the X-FE approximation of displacement in enriched elements and the formulation of dynamic explicit solution method with the X-FEM. By taking 1-D dynamic X-FE analyses as an example, we examine the lumping techniques of mass matrix in enriched elements and the influence on numerical accuracy and critical time step in Chapter 3. To examine the applicability and validity of the image-based X-FEM, numerical examples of wave propagation in heterogeneous materials are presented in Chapter 4.
