Static Analysis of Functionally Graded Plates Subjected to Mechanical and Thermal Loads

Plates and shells made of functionally graded materials (FGMs) often find application in a high-temperature environment. In the literature, considerable effort has been directed towards the analysis of functionally graded plates using two-dimensional theories. Many of these analysis techniques are extensions to approaches used for fibre-reinforced plastic (FRP) laminates. They consider the effects of through-thickness strains since these can be significant in FRPs. Functionally graded materials (FGMs) are often made from metals and ceramics, however. The through-thickness moduli are of the same order as the in-plane moduli and therefore errors introduced by neglecting the effects of through-thickness strains are far smaller. Classical lamination theory (CLT) can consequently provide useful estimates of deflection and stresses in all but the thickest plates. CLT does not accommodate material properties that progressively change though. As a consequence, the usual approach is to discretize each layer of FGM into a large number of sub-layers and then use a constant set of material properties appropriate to each sub-layer. It is more convenient, however, to use a method that directly considers variation in material properties. This paper presents such an approach, formulated as an extension to classical lamination theory. The resulting equations accommodate any through-thickness variation in material properties and loading. The true variation in these parameters is approximated by polynomial series of sufficiently high order that good accuracy is ensured. The resulting mathematical problem can be explicitly formulated irrespective of the actual variation in material properties and loading. Comparisons against results from more sophisticated analyses demonstrate the convenience and accuracy of the method.