Functionally graded plates behave like homogeneous plates

In recent years many articles concerned with the mechanics of functionally graded plates have been published. Usually new analysis methods are developed to handle the continuous variation in material properties through the thickness of the plate and extensive results are presented. This article shows that no special tools are required because functionally graded plates behave like homogeneous plates. This simple result is developed using the classical plate theory and is shown to hold true when higher order plate theories or the three dimensional elasticity theory is used. The variation in material properties through the thickness of the plate introduces a coupling between the inplane and bending deformations which complicates the analysis. Here we show that by a proper choice of the reference surface, this coupling can be eliminated so that the bending of the plate is governed by the same equation of motion as that of homogeneous plates.