Ashraf M. Zenkour

Bending Analysis of Functionally Graded Sandwich Plates Under the Effect of Mechanical and Thermal Loads

The bending response of sandwich plates subjected to thermo-mechanical loads is studied. The sandwich plate faces are assumed to have isotropic, two-constituent (metal-ceramic) material distribution through the thickness, and the modulus of elasticity, Poissons ratio, and thermal expansion coefficient of the faces 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. Several kinds of sandwich plates are used, taking into account the symmetry of the plate and the thickness of each layer. Field equations for functionally graded sandwich plates whose deformations are governed by either the shear deformation theories or the classical theory are derived. Displacement functions that identically satisfy boundary conditions are used to reduce the governing equations to a set of coupled ordinary differential equations with variable coefficients. Exact solutions for functionally graded materials (FGMs) sandwich plates are presented. Numerical results of the sinusoidal, third-order, first-order, and classical theories are presented to show the effect of material distribution on the deflections and stresses. A wide variety of results is presented for the static response of sandwich plates under thermo-mechanical loads. The effects of thermo-mechanical loads and other parameters on the dimensionless deflections and axial and transverse shear stresses of an FGM sandwich plate are studied.

Analysis of Sandwich Plates by Generalized Differential Quadrature Method

We combine a layer-wise formulation and a generalized differential quadrature technique for predicting the static deformations and free vibration behaviour of sandwich plates. Through numerical experiments, the capability and efficiency of this strong-form technique for static and vibration problems are demonstrated, and the numerical accuracy and convergence are thoughtfully examined.

Thermal Buckling of Functionally Graded Plates Resting On Elastic Foundations Using the Trigonometric Theory

In this article, thermal buckling analysis of functionally graded material (FGM) plates resting on two-parameter Pasternaks foundations is investigated. Equilibrium and stability equations of FGM plates are derived based on the trigonometric shear deformation plate theory and includes the plate foundation interaction and thermal effects. The material properties vary according to a power law form through the thickness coordinate. The governing equations are solved analytically for a plate with simply supported boundary conditions and subjected to uniform temperature rise and gradient through the thickness. Resulting equations are employed to obtain the closed-form solution for the critical buckling load for each loading case. The influences of the plate aspect ratio, side-to-thickness ratio, gradient index, and elastic foundation stiffnesses on the buckling temperature difference are discussed.

ON VIBRATION OF FUNCTIONALLY GRADED PLATES ACCORDING TO A REFINED TRIGONOMETRIC PLATE THEORY

The displacement components are expressed by trigonometric series representation through the plate thickness to develop a two-dimensional theory. This trigonometric shear deformation plate theory is used to perform free-vibration analysis of a simply supported functionally graded thick plate. Lames coefficients and density for the material of the plate are assumed to vary in the thickness direction only. Effects of rotatory inertia are considered in the present theory and the vibration natural frequencies are investigated. The results obtained from this theory are compared with those obtained from a 3D elasticity analysis and various equivalent theories that are available. A detailed analysis is carried out to study the various natural frequencies of functionally graded material plates. The influences of the transverse shear deformation, plate aspect ratio, side-to-thickness ratio and volume fraction distributions are investigated.

Bending analysis of functionally graded sandwich plates using a simple four-unknown shear and normal deformations theory

A refined trigonometric higher-order plate theory is presented for bending analysis of simply supported functionally graded ceramic–metal sandwich plates. The effects of transverse shear strains as well as the transverse normal strain are taken into account. The number of unknown functions involved in the present theory is only four as against six or more in case of other shear and normal deformations theories. Several types of the present symmetric and non-symmetric sandwich plates are used. The faces are assumed to be functionally graded through the thickness, while the core layer is still homogeneous and made of an isotropic material. The present refined plate theory is used to derive the field equations of the functionally graded sandwich plates. 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.

ANALYTICAL SOLUTIONS FOR ROTATING EXPONENTIALLY-GRADED ANNULAR DISKS WITH VARIOUS BOUNDARY CONDITIONS

This paper presents accurate elastic solutions for rotating annular disks. A new material properties and density profile in exponential form containing four geometric parameters is proposed. Analytical solutions using this profile are obtained in terms of Whittakers functions for the elastic deformation of rotating annular disks. The inner and outer edges of the disk are considered to have combinations of clamped and free boundary conditions. Special cases of rotating annular disks are investigated, which include annular disks with constant thickness and constant density, exponentially variable elastic properties and density, and exponentially graded disks. For all cases studied, closed form solutions are obtained and numerical results are presented. The results include the radial displacement, circumferential and radial stresses of the four annular disk configurations for combinations of homogeneous and exponentially graded cases. The distributions of stresses and displacement are obtained and comparisons between different cases are made at the same angular velocity.

THE EFFECT OF TRANSVERSE SHEAR AND NORMAL DEFORMATIONS ON THE THERMOMECHANICAL BENDING OF FUNCTIONALLY GRADED SANDWICH PLATES

A thermomechanical bending analysis for a simply supported, rectangular, functionally graded material sandwich plate subjected to a transverse mechanical load and a through-the-thickness thermal load is presented using the refined sinusoidal shear deformation plate theory. The present shear deformation theory includes the effect of both shear and normal deformations and it is simplified by enforcing traction-free boundary conditions at the plate faces. Material properties and thermal expansion coefficient of the sandwich plate faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The equilibrium equations of different sandwich plates are given based on various plate theories. A number of examples are solved to illustrate the numerical results concern thermo-mechanical bending response of functionally graded rectangular sandwich plates. The influences played by transversal shear and normal deformations, plate aspect ratio, side-to-thickness ratio, volume fraction distributions, and thermal and mechanical loads are investigated.

A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment

A simplified three-unknown shear and normal deformations nonlocal beam theory for thermo-electro-magneto mechanical bending analysis of a nanobeam with a functionally graded material core and two functionally piezomagnetic layers is studied in this paper. The assumed structure is subjected to mechanical, thermal, electrical, and magnetic loads. An initial applied voltage and magnetic load is considered on the functionally graded piezomagnetic material layers. Eringen’s nonlocal constitutive equations are considered in the analysis. Governing equations are derived according to the present refined theory using the principle of virtual displacements. The numerical results including the deflection, electric, and magnetic potential distribution are calculated in terms of important parameters of the problem such as applied electric and magnetic potentials, two parameters of temperature distribution, and nonlocal parameter. The numerical results indicate that increase in applied electric potential increases the deflection unlike the applied magnetic potential that decreases the deflection. Furthermore, it can be concluded that increasing the nonlocal parameter leads to increase in the deflection.

Employing sinusoidal shear deformation plate theory for transient analysis of three layers sandwich nanoplate integrated with piezo-magnetic face-sheets

In this paper, based on the sinusoidal shear deformation plate theory, equations of motion for a sandwich nanoplate containing a nano core and two integrated piezo-magnetic face-sheets are derived. The piezo-magnetic face-sheets are subjected to three dimensional electric and magnetic potentials. Nonlocal piezo-magneto-elastic relations are derived in a thermal environment. Hamiltons principle is used to derive seven equations of motion in terms of three deformation components of mid-surface, two shear components and electric and magnetic potentials. Natural frequencies of the sandwich nanoplate are derived in terms of nonlocal parameter. After finding solutions to the governing equations of motion, the effect of important parameters of the nanoplate are investigated on the mechanical, electrical and magnetic components of the nanoplate. Based on the present study, with increasing applied electric potential, dimensionless deflection is decreased and maximum electric and magnetic potentials are increased. Furthermore, with increasing applied magnetic potential, deflection is increased and maximum electric and magnetic potentials are decreased significantly. The numerical results of this problem indicate that one can control deformation or stress in the nano structure by changing the applied electric and magnetic potentials.

Three-dimensional Elasticity Solution for Uniformly Loaded Cross-ply Laminates and Sandwich Plates

This article establishes the bending problem of cross-ply laminated plates using the three-dimensional elasticity equations as well as the technique based on the state space concept. It presents a wide variety of results for the symmetric and antisymmetric analyses of rectangular multilayer plates subjected to a sinusoidally/uniformly distributed load (SDL/UDL). In addition, this study provides a strong mathematical tool allowing one to determine, in an exact and unified manner, the state of stress and displacement of cross-ply laminated composites and sandwich plates. The well-known results (given in Pagano ((1970), Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates, Journal of Composite Materials, 4(1): 20—24.) and Pagano and Hatfield ((1972), Elastic Behaviour of Multilayered Bidirectional Composites, AIAA Journal, 10(12): 931—933.) due to the exact three-dimensional elasticity solution are in fact special cases of the present technique.