Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories

Abstract

We derive field equations for a functionally graded plate whose deformations are governed by either the first-order shear deformation theory or the third-order shear deformation theory. These equations are further simplified for a simply supported polygonal plate. An exact relationship is established between the deflection of the functionally graded plate and that of an equivalent homogeneous Kirchhoff plate. This relationship is used to esplicitly express the displacements of a plate particle according to the first-order shear deformation theory in terms of the deflection of a homogeneous Kirchhoff plate. These relationships can readily be used to obtain similar correspondences between the deflections of a transversely laminated plate and a homogeneous Kirchhoff plate.