A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate

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.

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

A review of theories for the modeling and analysis of functionally graded plates and shells

Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory

Stress, vibration and buckling analyses of FGM plates—A state-of-the-art review

Bending analysis of functionally graded plates using the two variable refined plate theory is presented in this paper. The number of unknown functions involved is reduced to merely four, as against five in other shear deformation theories. The variationally consistent theory presented here has, in many respects, strong similarity to the classical plate theory. It does not require shear correction factors, and gives rise to such transverse shear stress variation that the transverse shear stresses vary parabolically across the thickness and satisfy shear stress free surface conditions. Material properties of the plate are assumed to be graded in the thickness direction with their distributions following a simple power-law in terms of the volume fractions of the constituents. Governing equations are derived from the principle of virtual displacements, and a closed-form solution is found for a simply supported rectangular plate subjected to sinusoidal loading by using the Navier method. Numerical results obtained by the present theory are compared with available solutions, from which it can be concluded that the proposed theory is accurate and simple in analyzing the static bending behavior of functionally graded plates.

A two variable refined plate theory for the bending analysis of functionally graded plates

This paper presents a theoretical investigation in free vibration of a functionally graded beam (FGB) which has a variable cross-section. It is assumed that material properties vary along the beam thickness only according to exponential distributions (it is simply called E-FGB). The governing equation is reduced to an ordinary differential equation in spatial coordinate for a family of cross-section geometries with exponentially varying width. Analytical solutions of the natural frequencies are obtained for E-FG beams with clamped-free, hinged-hinged, and clamped-clamped end supports. Results show that the non-uniformity in the cross-section and the inhomogeneity in material properties influence the natural frequencies. It is also shown that, all other parameters remaining the same, the natural frequencies of E-FG beams are always proportional to those of homogeneous isotropic beams. Therefore, one can predict the behaviour of E-FG beams knowing that of similar homogeneous beams.

Hichem Abdesselem Belhadj

Papers

A two variable refined plate theory for the bending analysis of functionally graded plates

Free Vibration Behavior of Exponential Functionally Graded Beams with Varying Cross-section

The thermal effect on vibration of zigzag single walled carbon nanotubes using nonlocal Timoshenko beam theory

Free vibration analysis of thin and thick-walled FGM box beams