Extension of the de Saint Venant and Kirchhoff theories to functionally graded materials

Functionally graded materials (FGMs) are special composites in which the volume fraction of constituent materials varies gradually, giving continuously graded mechanical properties. The aim of the present paper is the extension of the de Saint Venant's theory to axial load, bending and torsional moments, as well as to uniaxial or biaxial shears, from homogeneous members to FGM composite beams. The study is carried out in a simple and systematic way: its main assumption is the conservation of the plane sections. We will focus our attention on stresses and stored energy for FGM beams, the strains being simply derived by the linear elastic isotropic constitutive laws. Such approach is finally extended to plates in flexure, revisiting the Kirchhoff's theory. © 2007/9 IOS Press and the authors. All rights reserved.