Three-dimensional modal, dynamic, and wave propagation analyses of functionally graded solids

Date of Completion

January 2009


Applied Mechanics|Engineering, Civil




Modal, dynamic, and wave propagation behavior of three-dimensional (3D) functionally graded (FG) solids is studied using explicit (serial and parallel) finite element method, developed in-house, within the framework of linear elasticity. Modal analysis of 3D FG beams is obtained using finite element method (FEM) and Rayleigh-Ritz method. The natural frequencies obtained vary considerably with material gradation, more so for the lower modes than for the higher modes. Poisson's ratio considerably affects the torsional natural frequencies of the graded beams. The effect of sampling material properties at the element centroid than at the Gaussian integration point on the natural frequencies affects only certain type of graded beam. Transient dynamic behavior of a 3D homogeneous cantilever beam under sinusoidal loading is verified using the explicit FEM. Material gradation is found to considerably affect the dynamic response of the beam. Three numerical examples are studied to obtain the effects of gradation on the wave propagation behavior of 3D FG solids and to verify the explicit parallel FEM. In the first example, wave propagation in a 3D FG bar under impact is studied. Poisson's ratio and boundary conditions affect the stress behavior of the 3D homogeneous and FG bars. The second example is a three-point bending beam made of epoxy and glass phases under low velocity impact. Bending stress history for the beam with higher values of material properties at the loading edge is consistently higher than that of the homogeneous beam and the beam with lower values of material properties at the loading edge. Larger bending stresses for the former beam may indicate earlier crack initiation time which was proven by experiments performed by other researchers. The third example is that of an uncracked graded Kalthoff and Winkler plate under velocity impact. The stress evolution for the homogeneous plate compares reasonably well with the results obtained using a commercial software package ABAQUS. Dynamic stress behavior differs considerably for the three types of material gradation considered. Transient thermal stress analysis of a 3D homogeneous plate under 1D temperature loading is verified using an implicit FEM developed in-house. ^