Analytical solution for bending analysis of functionally graded plates

A theoretical formulation, of Navier solutions of rectangular plates based on a new higher order shear deformation model is presented for the static response of functionally graded plates (FGPs). This theory enforces traction free boundary conditions at plate surfaces. Shear correction factors are not required because a correct representation of transverse shearing strain is given. Unlike any other theory, the number of unknown functions involved is only four, as against five in cases of other shear deformation theories. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Numerical illustrations concern the flexural behavior of FG plates with metal–ceramic composition. Parametric studies are performed for varying ceramic volume fractions, volume fraction profiles, aspect ratios and length to thickness ratios. Results are verified with available results in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static bending behavior of functionally graded plates.