In this paper, an efficient and simple higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton’s principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with 3-dimensional and quasi-3-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates

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

In this work, various higher-order shear deformation plate theories for wave propagation in functionally graded plates are developed. Due to porosities, possibly occurring inside functionally graded materials (FGMs) during fabrication, it is therefore necessary to consider the wave propagation in plates having porosities in this study. The developed refined plate theories have fewer number of unknowns and equations of motion than the first-order shear deformation theory, but accounts for the transverse shear deformation effects without requiring shear correction factors. The rule of mixture is modified to describe and approximate material properties of the functionally graded plates with porosity phases. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton

Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories

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

In the present work, a simple and refined trigonometric higher-order beam theory is developed for bending and vibration of functionally graded beams The beauty of this theory is that, in addition to modeling the displacement field with only 3 unknowns as in Timoshenko beam theory, the thickness stretching effect (ez ≠ 0) is also included in the present theory Thus, the present refined beam theory has fewer number of unknowns and equations of motion than the other shear and normal deformations theories, and it considers also the transverse shear deformation effects without requiring shear correction factors The neutral surface position for such beams in which the material properties vary in the thickness direction is determined Based on the present refined trigonometric higher-order beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses

A new simple shear and normal deformations theory for functionally graded beams

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

The thermo-mechanical bending behavior of the antisymmetric cross-ply laminates is examined using a new simple four variable trigonometric plate theory The proposed theory utilizes a novel displacement field which introduces undetermined integral terms and needs only four variables The validity of the present model is proved by comparison with solutions available in the literature

Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory

This work presents a simplified higher order shear deformation theory (HSDT) for thermal buckling analysis of cross-ply laminated composite plates. Unlike the existing HSDT, the present one has a new displacement field which introduces undetermined integral terms and contains only four unknowns. Governing equations are derived from the principle of the minimum total potential energy. The validity of the proposed theory is evaluated by comparing the obtained results with their counterparts reported in literature. It can be concluded that the proposed HSDT is accurate and simple in solving the thermal buckling behavior of laminated composite plates.

Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT

In the present work, the buckling behavior of a single-layered graphene sheet (SLGS) embedded in visco-Pasternak\' s medium is studied using nonlocal four-unknown integral model. This model has a displacement field with integral terms which includes the effect of transverse shear deformation without using shear correction factors. The visco-Pasternak\'s medium is introduced by considering the damping effect to the classical foundation model which modeled by the linear Winkler\'s coefficient and Pasternak\' s coefficients, damping parameter, and mode numbers on the buckling response of the SLGSs are studied and discussed.

Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model

Two refined displacement models, RSDT1 and RSDT2, are developed for a bending analysis of functionally graded sandwich plates. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The developed models are variationally consistent, have strong similarity with classical plate theory in many aspects, do not require shear correction factor, and give rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress-free surface conditions. The accuracy of the analysis presented is demonstrated by comparing the results with solutions derived from other higher-order models. The functionally graded layers are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity, Poisson’s ratio of the faces, and thermal expansion coefficients are assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. Numerical results for deflections and stresses of functionally graded metal–ceramic plates are investigated. It can be concluded that the proposed models are accurate and simple in solving the bending behavior of functionally graded plates.

https://atpw.files.wordpress.com/2013/03/c-9_atpw-2012_a-b-e-abbastwo-new-refined-shear-displacement-models.pdf

Habib Hebali

Papers

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

Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory

Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT

Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model

Two new refined shear displacement models for functionally graded sandwich plates