Finite element formulation for bending of FG plates using four-variable refined plate theory

In this paper, a finite element formulation based on four-variable refined plate theory for bending analysis of functionally graded plates is presented. The four-variable refined plate theory predicts parabolic variation of transverse shear stresses across the plate thickness and stisfies zero traction condition on the surfaces of the plate without using the shear correction factor. The governing equations are drived using the minimum potential energy principle and the weak form equations are constructed. A new 4-node nonconforming rectangular plate element with eight degrees of freedom at each node is considered for descritizing the domain. Material properties of the plate are assumed to vary through the thickness according to a simple power-law distribution in terms of the volume fractions of the constituents. A finite element code is written using MATLAB software. Several benchmark problems including simply supported functionally graded plates subjected to uniformly or sinusoidally distributed mechanical load are solved. The results obtained in this study are in good agreement wih available analytical solutions which proves the accuracy and efficiency of present finite element formulation. The results also show that the present refined theory is accurate for moderately thick plates in predicting in-plane and transverse displacements and stresses. Also the effects thickness ratio and volume fraction ratio on the results are investigated.