Three-dimensional analysis of an all-round clamped plate made of functionally graded materials (original) (raw)
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Bending behaviour of FGM plates via a simple quasi-3D and 2D shear deformation theories
2020
This article investigates the static behaviour of functionally graded (FG) plates sometimes declared as advanced composite plates by using a simple and accurate quasi-3D and 2D hyperbolic higher-order shear deformation theories. The properties of functionally graded materials (FGMs) are assumed to vary continuously through the thickness direction according to exponential law distribution (E-FGM). The kinematics of the present theories is modeled with an undetermined integral component and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate; therefore, it does not require the shear correction factor. The fundamental governing differential equations and boundary conditions of exponentially graded plates are derived by employing the static version of principle of virtual work. Analytical solutions for bending of EG plates subjected to sinusoidal distributed load are obtained for simply supported boundary conditions using Navier\'is solu...
Analysis of functionally graded plates using higher order shear deformation theory
This work addresses a static analysis of functionally graded material (FGM) plates using higher order shear deformation theory. In the theory the transverse shear stresses are represented as quadratic through the thickness and hence it requires no shear correction factor. The material property gradient is assumed to vary in the thickness direction. Mori and Tanaka theory (1973) [1] is used to represent the material property of FGM plate at any point. The thermal gradient across the plate thickness is represented accurately by utilizing the thermal properties of the constituent materials. Results have been obtained by employing a C° continuous isoparametric Lagrangian finite element with seven degrees of freedom for each node. The convergence and comparison studies are presented and effects of the different material composition and the plate geometry (side-thickness, side–side) on deflection and temperature are investigated. Effect of skew angle on deflection and axial stress of the plate is also studied. Effects of material constant n on deflection and the temperature distribution are also discussed in detail.
Various plate theory used in the analysis of FGMs-A review
Elsevier, 2022
This article reviews different plate theories which are used in the structural analysis of various functionally graded structures like shells/plates. The different plate theories are compared by introducing displacement field variables. It was found that first-order shear deformation theory (FSDT) and higherorder shear deformation theory (HSDT) are the most widely applicable theories for the structural examination of moderately thin functionally graded materials (FGMs) compared to classical laminate plate theory (CLPT). Since most researchers implemented two-dimensional theories which save considerable computational time and cost compared to three-dimensional theories. Therefore, this study is more focused on 2D-based theories. The end result of this study can be highly useful for researchers and designers in selecting appropriate theories to examine the structural behaviour of different composite materials.
A Theoretical Analysis for Static and Dynamic Behavior of Functionally Graded Plates
2012
Theoretical formulation, Navier’s solutions of rectangular plates based on a new higher order shear deformation model are presented for the static and dynamic analysis of functionally graded plates (FGPs). This theory enforces traction free boundary conditions at plate surfaces. Shear correction factors are not required because a correct representation of transverse shearing strain is given. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Numerical illustrations concern flexural behavior of FG plates with Metal–Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction profiles, aspect ratios and length to thickness ratios. Results are verified with available ...
A displacement-based, higher order shear and normal deformations theory (HOSNT) is used to analyse the thick functionally graded (FG) plates in which mechanical properties are changing smoothly with the plate's thickness coordinate. A more realistic parabolic distribution of transverse shear strains through thickness of plate is ensured in the presented formulation. The influence of transverse normal strain on bending responses of FG plates is examined in this study. Functionally graded materials (FGMs), although heterogeneous, are idealized as continua with their mechanical properties changing smoothly with respect to spatial coordinates. The material properties of FG plates are assumed to be varying through thickness of plate in a continuous manner. Poisson's ratio of FG plates is assumed to be constant, but their Young's modulii are considered to vary continuously in thickness direction according to the volume fraction of its constituents which is mathematically modelled as an exponential function. The governing equations of equilibrium for static analysis of FG plates are obtained using principle of minimisation of potential energy (PMPE) employing HOSNT. Navier solution method is used to solve the governing differential equations of equilibrium. It is thought that the presented results would be a reference for other researchers to compare their results.
Mathematical Approach for Mechanical Behaviour Analysis of FGM Plates on Elastic Foundation
MDPI, 2022
This paper presents the flexural analysis of functionally graded plates resting on elastic foundations using new two-dimensional (2D) and quasi-three-dimensional (quasi-3D) higher order shear deformation theories. The main interesting feature of this theory is that it proposes a new displacement field with undetermined integral variables which involves only five unknown functions, unlike other shear and normal deformation theories, hence making it easier to use. A parabolic transverse shear deformation shape function satisfying the zero shear stress conditions on the plate outer surfaces is considered. The elastic foundation follows the Pasternak mathematical model. The material properties change continuously across the thickness of the FG plate using different distributions: power law, exponential, and Mori–Tanaka models. The governing equations of FG plates subjected to sinusoidal and uniformly distributed loads are established through the principle of virtual works and then solved via Navier’s procedure. In this work, a detailed discussion on the influence of material composition, geometric parameters, stretching effect, and foundation parameters on the deflection, axial displacements, and stresses is given, and the obtained results are compared with those published in previous works to demonstrate the accuracy and the simplicity of the present formulations. The different obtained results were found to be in good agreement with the available solutions of other higher-order theories. The proposed model is able to represent the cross section warping in the deformed shape and to demonstrate the validity and efficiency of the approach, the findings reported herein prove that this theory is capable of predicting displacements and stresses more accurately than other theories, as its results are closer when compared to numerical methods reported in other literatures.
Static Response of Functionally Graded Plates using Higher Order Theories
IOP conference series, 2018
This work presents an assessment of higher order theories for the static response of functionally graded plates. The governing equations, variationally consistent boundary conditions, force and moment resultants of higher order shear deformable theories are derived using principle of virtual work. Material properties are assumed to vary smoothly in the thickness direction with power law variation of ceramic volume fraction. The effective material properties of FG material are obtained using rule of mixture as well as Mori-Tanaka homogenization scheme. Analytical solution using a double Fourier series expansion is obtained for simply supported plates. The computer program has been developed in MATLAB and the results are validated by comparing with the results available in the literature. The values of deflection, inplane and transverse stresses are presented for different theories, span to thickness ratio and inhomogeneity parameter.
Static and Vibration Analysis of FGM Plates: A Critical Review
International Journal for Research in Applied Science & Engineering Technology (IJRASET), 2023
Recently a new material has been emerged with variation of material properties particularly across the thickness. Such class of materials is called functionally graded materials. The concept of functionally graded material was proposed in 1984 by materials scientists as a means of preparing thermal barrier materials. Since then functionally graded materials are being increasingly used in the aeronautical and aerospace industry as well as in other fields of modern technology. This paper presents a comprehensive review of the various methods used to study the static and dynamic behaviour of functionally graded material plates. Both analytical and numerical methods are considered. The effect of variation of material properties through the thickness, type of load case, boundary conditions, edge ratio and side-to thickness ratio on the behaviour of functionally graded material plates are discussed. The main objective of this paper is to serve the interests of researchers and engineers already involved in the analysis and design of functionally graded material structures.
A higher-order shear and normal deformation functionally graded plate model: some recent results
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