Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory

Abstract

A new simple "four-variable shear deformation" plate model is proposed in this work to demonstrate the hygro-thermal environment effects on dynamic and buckling of functionally graded material "sandwich plates" supported by "Winkler-Pasternak" elastic foundations. Equations of motion are obtained from Hamilton's principle

Static and dynamic characteristics of nano-reinforced 3D-fiber metal laminates using non-destructive techniques

“…Since in this study the fundamental bending frequency of the beam is of interest, only the first value for γ n was computed numerically, yielding γ 1 = 4.73. Moreover, D 11 obtained from the experimental data (i.e., load–deflection curves) was contrasted with the analytical solution calculated using equation (4) [9,30,80,81]where Q is the transformed stiffness matrix of each ply (layer) of the composite material; Z k and Z k -1 refer to the distances measured from the mid-plane of the 3DFGF or 3DFML panels to the bottom and top of each plies (layers), respectively, and k and n indicate correspondingly the individual ply (layer) index and total number of plies in the panel.…”

Thermal buckling analysis of cross-ply plates based on new displacement field

“…Younsi et al (2018) proposed two-dimensional and quasi-three-dimensional higher-order shear deformation theory for bending and free vibration investigation of functionally graded plates based on hyperbolic displacement function; Riad Hamza-Cherif et al (2018) analyzed Euler-Bernoulli beam model with different boundary conditions to predict the vibration of a single-walled carbon nanotube embedded under thermal effect, using Differential Transform Method; A. Bouhadra et al (2018) improved a higher shear deformation theory to investigate plates made from functionally graded, by accounting in-plane displacements that have undetermined integral terms and a parabolic variation for vertical displacement through the thickness; M. Benchohra et al (2018) developed a quasi-3D sinusoidal shear deformation theory accounting for shear deformation and thickness-stretching influences using a trigonometric function for all displacements distribution along thickness, to analyze bending and free vibration for simply supported functionally graded plates; Moussa Abualnour et al 2019) used a simple quasi-3D shear deformation theory based on a displacement field that has five variables and reported new kinematics that contain undetermined integral variables, for thermomechanical bending analysis of functionally graded material sandwich plates; Hadjira Hellal et al (2019) developed a simple "four-variable shear deformation" plate model, which has a displacement field containing integral terms and transverse shear stress trigonometric variation to study the hygrothermal environment effects on buckling and dynamic of plates rest on elastic foundations; Zoulikha Boukhlif et al ( 2019) investigated free vibration of functionally graded (FG) plates resting on elastic foundation using a simple quasi-3D higher shear deformation theory, which considered variation of displacement along thickness and has only four unknowns; Boulefrakh Laid et al (2019) used quasi-3D hyperbolic shear deformation model for static and dynamic analyses of functionally graded plates resting on foundations with damping effect; Sabrina Boutaleb et al ( 2019) studied free vibration analysis of the functionally graded rectangular nanoplates, using theory of nonlocal elasticity based on the quasi-3D high shear deformation theory, and a cubic displacement function is used along the thickness; Zaoui et al ( 2019) developed a two-dimensional and quasi-three-dimensional shear deformation theories that have a novel displacement field, which includes undetermined integral terms and contains fewer unknowns to model the free vibration of FG plates resting on elastic foundations.…”

“…Abdelkader developed a refined quasi-three-dimensional shear deformation theory that has a number of unknowns and governing equations, only four fewer than unknown displacement functions taken by other theories, to study thermomechanical response of functionally graded sandwich plates; Lynda Amel Chaabane et al ( 2019) used a hyperbolic shear deformation theory to analyze static and dynamic behavior of simply supported FG-beam resting on Winkler-Pasternak foundation types; Fouad Bourada et al (2019) investigated free vibration analysis of simply supported perfect and imperfect (porous) FG beams using a high-order trigonometric deformation theory that has three unknown and has a parabolic shear deformation variation along the thickness; Mohammed Medani et al ( 2019) investigated static and dynamic behavior of plate made from Functionally Graded Carbon Nanotubes, reinforced porous sandwich (PMPV) polymer, and nanocomposite plate, using first-order shear deformation theory; Rafik Meksi et al (2019) developed a new shear deformation plate theory based on a new displacement field containing integrals, which has four variables, and quasi-parabolic variation of transverse shear stress, to analyze the bending, buckling, and natural frequencies functionally graded material sandwich plates.…”

Natural frequency, damping and forced responses of sandwich plates with viscoelastic core and graphene nanoplatelets reinforced face sheets

“…Belalia (2019) investigated the free vibrations of the geometrically nonlinear functionally graded sandwich plates with ceramic core by von Karman’s assumptions. Hellal et al (2019) examined the hygro-thermal environmenal effects on dynamic and buckling of functionally graded sandwich plates resting on elastic foundations, and Joseph and Mohanty (2019) employed the finite element method to study the free vibration of a three-layered sandwich plate with the viscoelastic core layer and functionally graded material constraining layer. Meksi et al (2019) developed a new theory of shear deformation plate to study the free vibration, buckling and bending responses of functionally graded sandwich plates.…”