A higher-order hyperbolic shear deformation plate model for analysis of functionally graded materials

This paper presents a new higher-order hyperbolic shear deformation theory for analysis of functionally graded plates. In this theory, the transverse shear stresses account for a hyperbolic distribution and satisfy the free-traction boundary conditions on the top and bottom surfaces of the plate. By making a further assumption, the present theory contains only four unknowns and its governing equations is therefore reduced. Equations of motion are derived from Hamilton's principle and Navier-type analytical solutions for simply-supported plates are compared with the existing solutions to verify the validity of the developed theory. The material properties are continuously varied through the plate thickness by the power-law and exponential form. Numerical results are obtained to investigate the effects of the power-law index and side-to-thickness ratio on the deflections, stresses, critical buckling load and natural frequencies.