Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position

A new first-order shear deformation theory is developed for bending and dynamic behaviors of functionally graded plates. Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher order shear deformation theories. The equations governing the axial and transverse deformations of functionally graded plates are derived based on the present first-order shear deformation plate theory and the physical neutral surface concept. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. To examine accuracy of the present formulation, several comparison studies are investigated. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of functionally graded plates.