Exact 3-D Stress and Stiffness Analysis of Functionally Graded Sandwich Plates Using Sampling Surfaces Method

2014 ◽  
Author(s):  
Mehdi Darabi ◽  
Rajamohan Ganesan
Keyword(s):  
Volume Fraction ◽  
Plate Theory ◽  
Three Dimensional ◽  
Core Layer ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Stress Distributions ◽  
Power Law Distribution ◽  
Approach Zero ◽  
Comparison Of The Results

In the present work, the three-dimensional analysis for the deflection and stress distributions of functionally graded ceramic–metal sandwich plates is developed based on the method of sampling surfaces (SaS). In accordance with this method, into each layer of the plate, reference surfaces that are not equally spaced and are parallel to the mid-surface of the plate are introduced, and the displacement vectors of these surfaces are chosen as unknown functions. Such a choice allows the representation of the governing equations of the proposed higher order layer-wise plate theory in a very compact form and also permits the derivation of strain–displacement relationships correctly describing all motions including the rigid-body motions of the functionally graded plate. Hence the 3D elasticity problem of the thick plate is efficiently solved. The material properties of sandwich plate’s face layer are assumed to be that of a two-constituent material that vary continuously through the thickness of the face sheet according to a power law distribution of the volume fraction of the constituents. The core layer is homogeneous and made of an isotropic ceramic material. The effects of the volume fraction of the material constituents and their distribution on the deflections and, in particular, the 3-D stress distributions as well as the effects of the length-to-width and length-to-thickness ratios of the plate are investigated. Comparison of the results of the present work with the results available in existing literature is carried out for a benchmark problem. It is shown that considering large number of SaS, which are located at interfaces and Chebyshev polynomial nodes, the accuracy of the solutions can be improved significantly wherein the error will approach zero value as the total number of surfaces in each layer become very large.

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

2009 ◽  
Vol 01 (04) ◽  
pp. 667-707 ◽  
Author(s):  
ASHRAF M. ZENKOUR
Keyword(s):  
Shear Deformation ◽  
Sandwich Plate ◽  
Volume Fraction ◽  
Mechanical Load ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Power Law Distribution ◽  
Equilibrium Equations

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.

Axisymmetric Solutions of Functionally Graded Circular and Annular Plates Using Second-Order Shear Deformation Plate Theory

2006 ◽  
Author(s):  
Ali Reza Saidi ◽  
Shahab Sahraee
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Second Order ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Classical Plate Theory ◽  
Maximum Displacement ◽  
Shear Deformation Plate Theory ◽  
Axisymmetric Bending

In this paper, axisymmetric bending and stretching of functionally graded solid circular and annular plate is studied based on the second-order shear deformation plate theory (SST). The solutions for deflections, force and moment resultants of the second-order theory are presented in terms of the corresponding quantities of the isotropic plates based on the classical plate theory from which one can easily obtain the SST solutions for axisymmetric bending of functionally graded circular plates. It is assumed that the mechanical properties of the functionally graded plates vary continuously through the thickness of the plate and obey a power law distribution of the volume fraction of the constituents. Numerical results for maximum displacement are presented for various percentages of ceramic-metal volume-fractions and have been compared with those obtained from first-order shear deformation plate theory (FST).

POSTBUCKLING RESPONSE OF FUNCTIONALLY GRADED RECTANGULAR PLATES SUBJECTED TO THERMO-MECHANICAL LOADING

2007 ◽  
Vol 07 (03) ◽  
pp. 519-541 ◽  
Author(s):  
K. K. SHUKLA ◽  
K. V. RAVI KUMAR ◽  
RAMESH PANDEY ◽  
Y. NATH
Keyword(s):  
Mechanical Loading ◽  
Volume Fraction ◽  
Plate Theory ◽  
Functionally Graded ◽  
Buckling Load ◽  
Rectangular Plates ◽  
Power Law Distribution ◽  
Transverse Temperature ◽  
The Stability ◽  
Plane Temperature

The present work deals with the stability analysis of shear deformable functionally graded rectangular plates subjected to thermo-mechanical loads. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. An analytical approach based on fast converging Chebyshev polynomials is presented. The formulation is based on first-order shear deformation plate theory and von-Karman nonlinearity. The temperature-dependent thermal and mechanical properties of FGM plate are considered. The variations in the buckling load/temperature due to various parameters are studied. The postbuckling response of the clamped FGM plate, subjected to in-plane edge compressive mechanical loading (uniaxial, biaxial, shear), thermal (uniform in-plane temperature, transverse temperature gradient) and thermo-mechanical loading are presented. It is observed that volume fraction index greatly affects the buckling load/temperature of the plate.

A quasi-three-dimensional isogeometric model for porous sandwich functionally graded plates reinforced with graphene nanoplatelets

2021 ◽  
pp. 109963622110204
Author(s):  
Nam V Nguyen ◽  
H Nguyen-Xuan ◽  
Jaehong Lee
Keyword(s):  
Free Vibration ◽  
Plate Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Core Layer ◽  
Graphene Nanoplatelets ◽  
Functionally Graded ◽  
Plate Structures ◽  
Graded Materials ◽  
Fg Plates

The purpose of this study is to present a quasi-three-dimensional (quasi-3D) shear deformation theory for static bending and free vibration analyses of porous sandwich functionally graded (FG) plates with graphene nanoplatelets (GPLs) reinforcement. In addition, we propose a novel sandwich plate model with various outstanding features in terms of structural performance. The quasi-3D theory-based isogeometric analysis (IGA) in conjunction with refined plate theory (RPT) is first exploited to capture adequately the thickness stretching effect for porous sandwich FG plate structures reinforced with GPLs. The Non-Uniform Rational B-Splines (NURBS)-based IGA is employed in order to describe exactly the geometry models as well as approximate the unknown field with higher-order derivatives and continuity requirements while the RPT model includes only four essential variables. The sandwich FG plates consist of a core layer containing internal pores reinforced by GPLs and two functionally graded materials (FGMs) skin layers. Effective mechanical properties can be evaluated by employing the Halpin-Tsai model along with the rule of mixture. Various combinations of two porosity distributions and three GPL dispersions in the core layer are thoroughly investigated. Several numerical investigations are conducted to examine the effects of several key parameters on the static bending and free vibration behaviors of sandwich FG plate structures.

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

2012 ◽  
Vol 28 (3) ◽  
pp. 439-452 ◽  
Author(s):  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Power Law ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Graded Material ◽  
Plate Aspect Ratio ◽  
Type V ◽  
Power Law Index

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

Characterization of the vibration, stability and static responses of graphene-reinforced sandwich plates under mechanical and thermal loadings using the refined shear deformation plate theory

2021 ◽  
pp. 109963622199386
Author(s):  
Hessameddin Yaghoobi ◽  
Farid Taheri
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Sheet Thickness ◽  
Analytical Investigation ◽  
Sandwich Plates ◽  
Simply Supported ◽  
Vibration Stability ◽  
Shear Deformation Plate Theory

An analytical investigation was carried out to assess the free vibration, buckling and deformation responses of simply-supported sandwich plates. The plates constructed with graphene-reinforced polymer composite (GRPC) face sheets and are subjected to mechanical and thermal loadings while being simply-supported or resting on different types of elastic foundation. The temperature-dependent material properties of the face sheets are estimated by employing the modified Halpin-Tsai micromechanical model. The governing differential equations of the system are established based on the refined shear deformation plate theory and solved analytically using the Navier method. The validation of the formulation is carried out through comparisons of the calculated natural frequencies, thermal buckling capacities and maximum deflections of the sandwich plates with those evaluated by the available solutions in the literature. Numerical case studies are considered to examine the influences of the core to face sheet thickness ratio, temperature variation, Winkler- and Pasternak-types foundation, as well as the volume fraction of graphene on the response of the plates. It will be explicitly demonstrated that the vibration, stability and deflection responses of the sandwich plates become significantly affected by the aforementioned parameters.

scholarly journals Weight optimisation of functionally graded beams using modified differential evolution

2019 ◽  
Vol 13 (2) ◽  
pp. 48-63 ◽  
Author(s):  
Pham Hoang Anh ◽  
Tran Thuy Duong
Keyword(s):  
Differential Evolution ◽  
Volume Fraction ◽  
Lightweight Design ◽  
Shear Deformation Theory ◽  
Numerical Approach ◽  
Functionally Graded ◽  
Parameter Distribution ◽  
Power Law Distribution ◽  
De Algorithm ◽  
Fgm Beam

In this article, an efficient numerical approach for weight optimisation of functionally graded (FG) beams in the presence of frequency constraints is presented. For the analysis purpose, a finite element (FE) solution based on the first order shear deformation theory (FSDT) is established to analyse the free vibration behaviour of FG beams. A four-parameter power law distribution and a five-parameter trigonometric distribution are used to describe the volume fraction of material constituents in the thickness direction. The goal is to tailor the thickness and material distribution for minimising the weight of FG beams while constraining the fundamental frequency to be greater than a prescribed value. The constrained optimisation problem is effectively solved by a novel differential evolution (DE) algorithm. The validity and efficiency of the proposed approach is demonstrated through two numerical examples corresponding to the four-parameter distribution and the five-parameter distribution.Keywords: FGM beam; lightweight design; frequency constraint; differential evolution.

scholarly journals Optimum response of functionally graded piezoelectric plates in thermal environments

2017 ◽  
Vol 35 (3) ◽  
pp. 606-617 ◽  
Author(s):  
Hossein Nourmohammadi ◽  
Bashir Behjat
Keyword(s):  
Power Law ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Plate Theory ◽  
Poisson Ratio ◽  
Functionally Graded ◽  
Sensors And Actuators ◽  
Thermal Environments ◽  
Functionally Graded Piezoelectric ◽  
Power Law Index

AbstractIn this article, the static response of the functionally graded piezoelectric (FGP) plates with piezoelectric layers (sandwich FGPM) is studied based on the first order shear deformation plate theory. The plate is under mechanical, electrical and thermal loadings and finite element method is employed to obtain the solution of the equation. All mechanical, thermal and piezoelectric properties, except Poisson ratio, obey the power law distribution through the thickness. By solving the governing equation, optimum value of power law index is investigated in each type of loading. The effects of different volume fraction index, layer arrangements, various boundary conditions and different loading types, are studied on the deflection of FGPM plate. It is inferred that, the correlations between the deflection, power law index and layer arrangement are completely different in the mechanical and thermal loading and the optimum value of the power law index should be selected in each case separately. This optimum values can be used as a design criterion to build a reliable sensors and actuators in thermal environments.

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