New Quasi-3D Hyperbolic Shear Deformation Theory for the Static and Free Vibration Analysis of Functionally Graded Plates

In this paper, a new quasi-three-dimensional (3D) hyperbolic shear deformation theory for the bending and free vibration analysis of functionally graded plates is developed. By dividing the transverse displacement into bending, shear, and thickness stretching parts, the number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Unlike any other theory, the number of unknown functions involved in displacement field is only five, as against six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to check the accuracy and efficiency of the present theory.