A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets

In this paper, a new higher-order shear and normal deformation theory for the bending and free vibration analysis of sandwich plates with functionally graded isotropic face sheets is developed. The number of unknown functions involved in the present theory is only five, as against six or more in case of other shear and normal deformation theories. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. The boundary conditions for the plate are assumed to be simply supported in all edges and in the static analysis, the plate is assumed to be subjected to a sinusoidally distributed load. Both symmetric and non-symmetric sandwich plates are considered. The equations of motion are obtained using Hamilton's principle. Numerical results of present theory are compared with three-dimensional elasticity solutions and other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and efficient in predicting the bending and free vibration responses of sandwich plates with functionally graded isotropic face sheets.