An optimized 2D kinematic model for flexure and free vibration analysis of functionally graded plates

In this paper, a new refined higher-order shear deformation theory "RHSDT" is presented for the flexure and free vibration analysis of functionally graded (FG) plates. The main feature of this model is that it relies on a simple and optimized 2D displacement field with only two unknown variables, even less than other shear deformation theories that involve three or more unknown variables. The current theory considers a hyperbolic non-linear shape function for satisfying exactly the zero shear stress conditions on the external plate surfaces without using a shear correction factor. The mechanical properties of FG plates are assumed to vary continuously through the thickness direction according to a power-law distribution "P-FGM" and an exponential-law distribution "E-FGM". The governing equations and boundary conditions of FG plates are derived by implementing Hamilton's principle. To verify the accuracy of the present theory, the analytical results computed for simply supported FG thick plates via the Navier-type technique are checked with those obtained by other shear deformation models and 3D elasticity solutions regarded in the literature. Additionally, the impact of significant parameters on the results of mechanical stresses and natural frequencies is discussed.