The use of graded finite elements in the study of elastic wave propagation in continuously nonhomogeneous materials

Finite elements with graded properties are used to simulate elastic wave propagation in functionally graded materials. The graded elements are formulated with continuously nonhomogeneous material property fields and compared to conventionally formulated homogeneous elements. An example problem is solved for the two-dimensional case to show the potential benefits of the graded formulation. It is observed that the conventional elements give a discontinuous stress field in the direction perpendicular to the material property gradient, while the graded elements give a continuous distribution. In the one-dimensional case, the solutions are compared to the analytical solutions by Chiu and Erdogan [J. Sound Vib. 222 (3) (1999) 453]. The results show that for identical levels of mesh refinement, the graded formulation produces similar spatial resolution, and temporal resolution for the range of boundary value problems studied. Observations are explained and their implications for numerical modeling are discussed.