Application of the spectral nite element method for elastic wave propagation problems in functionally graded materials

Resumo

This work is concerned with the numerical modeling of elastic wave propagation in a medium constructed with functionally graded materials (FGMs). The FGM is characterized by a gradual change in the material properties over the domain under consideration and its application has been growing in some science and engineering areas. In contrast to layered materials in which effects of reflection and refraction of waves still occur between layers (a situation not always desirable), materials that possess a continuous variation of their properties do not suffer from this drawback. Here, the time-domain elastodynamic equations in FGMs are numerically solved by means of the spectral finite element method based on the Gauss-Lobatto-Legendre points. Owing to the smooth transition of the material properties over the domain makes the SFEM quite suitable for this type of problem since material interfaces are not presented and, therefore, large elements can be easily employed. Furthermore, the SFEM can be viewed as a higher-order finite element method (FEM) and has been receiving great popularity for owning the FEM geometric flexibility in creating meshes among other numerical features such as less dispersion errors and mass lumping. At the end of the paper, a numerical example considering a FGM is presented, and the results are compared with those furnished by the the equivalent homogeneous and layered bi-material models to illustrate the difference of the models.