Efficient higher-order shear deformation theories for bending and free vibration analyses of functionally graded plates

Abstract

In this paper, various efficient higher-order shear deformation theories are presented for bending and free vibration analyses of functionally graded plates. The displacement fields of the present theories are chosen based on cubic, sinusoidal, hyperbolic, and exponential variations in the in-plane displacements through the thickness of the plate. By dividing the transverse displacement into the bending and shear parts and making further assumptions, the number of unknowns and equations of motion of the present theories is reduced and hence makes them simple to use. Equations of motion are derived from Hamilton's principle. Analytical solutions for deflections, stresses, and frequencies are ..