Functionally graded materials (FGM) have been designed and developed in many engineering parts that need to be super heat resistant ,such as thermal barrier materials for text for this section, aerospace structural applications and fusion reactors . FGM material properties vary smoothly and continuously from one surface to the other.

An analytical approach for mechanical stability analysis of functionally graded plate is presented. The equilibrium and stability equation are derived according to the first order shear deformation theory. These equations are solved for the functionally graded plate with variable thickness under different types of mechanical loading. The excellent accuracy of the present results with those available in the literature. Furthermore the effects of power of functionally graded material, parameter material, aspect ratio, loading types on the critical buckling load of the functionally graded rectangular plate are studied and discussed [1].

the realization of the plates in the different fields of use imposes a varied geometry the reason for which we are studying the varied thickness, even though thickness variation are rather rare in literature..