scholarly journals Functionally Graded Panels: A Review

2020 ◽  
pp. 36-43
Author(s):  
C. Pany Sreeju Nair S B
Keyword(s):  
Free Vibration ◽  
Power Law ◽  
Material Properties ◽  
Structural Model ◽  
Constitutive Relations ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Power Law Distribution ◽  
Literature Study ◽  
Static And Dynamic Analysis

Functionally gradedmaterials (FGMs) are not homogeneous materials. It consists of different(two or more) materials, engineered to have a continuously varying spatial composition profile. FGM is the one that can solve practical problems arising from the production and application of a new type of composite material. This paper describes the overview of FGM basic concepts, classification, properties, and its modeling which may focus on the static and dynamic analysis of functionally graded panels. The effective material properties of functionally graded materials for the panel are graded in the thickness direction from the bottom surface to the top surface according to the power-law distribution of volume fractions of the constituents. The use of structures like beams, plates, and shells, which are made from functionally graded (FG) materials, is increasing because of the smooth variation of material properties along with preferred directions. This variation gives continuous stress distribution in the FG structures. Therefore, an FGM can be effectively used in avoiding corrosion, fatigue, fracture, and stress corrosion cracking. The paper covers the literature study on static, buckling and free vibration, thermo-mechanical analysis of FGM panel. From this literature study it is found that, analysis of these problems is made using the constitutive relations and governing equations associated with the classical laminated theory structural model, the FSDT model, the HSDT model,Reissner and Sander theory,differential quadrature, finite element method and closed form solutions. Results are availableon different geometrical dimensional ratios variations, power-law index value n variationsand simply supported,clamped, free edges boundary conditionswith its combinations for FG panels. Lesser literatures are available for different edge boundary conditions such as SCSC, CSCS,SSSC, SFSF, SSSF, SCSF on curved panelfor free vibration, buckling and thermo-structural analysis.

Free Vibration Responses of Functionally Graded Spherical Shell Panels Using Finite Element Method

2013 ◽  
Author(s):  
Vishesh Ranjan Kar ◽  
Subrata Kumar Panda
Keyword(s):  
Mathematical Model ◽  
Free Vibration ◽  
Spherical Shell ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Power Law Distribution ◽  
Vibration Responses ◽  
Support Conditions

Free vibration responses of functionally graded spherical shell panels are investigated in the present article. A general mathematical model is developed based on higher order shear deformation theory mid-plane kinematics. The effective material properties are graded in the thickness direction according to a power-law distribution and it varies continuously from metal (bottom surface) to ceramic (top surface). The model is discretized using a nine noded quadrilateral Lagrangian element. A convergence test has been done with different mesh refinement and compared with the available published results. In addition to that the present study includes an ANSYS model check with the developed mathematical model to show the efficacy. New results are computed for different parameters such as volume fraction, thickness ratio, curvature ratio and support conditions which indicates the effect of parametric study on non-dimensional frequency parameters.

Bending, Buckling and Free Vibration Analysis of Size-Dependent Nanoscale FG Beams Using Refined Models and Eringen’s Nonlocal Theory

2020 ◽  
Vol 12 (01) ◽  
pp. 2050007 ◽  
Author(s):  
Atteshamuddin S. Sayyad ◽  
Yuwaraj M. Ghugal
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Volume Fraction ◽  
Constitutive Relations ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Solution Technique ◽  
Small Scale ◽  
Nonlocal Beam

In this study, a theoretical unification of twenty-one nonlocal beam theories are presented by using a unified nonlocal beam theory. The small-scale effect is considered based on the nonlocal differential constitutive relations of Eringen. The present unified theory satisfies traction free boundary conditions at the top and bottom surface of the nanobeam and hence avoids the need of shearing correction factor. Hamilton’s principle is employed to derive the equations of motion. The present unified nonlocal formulation is applied for the bending, buckling and free vibration analysis of functionally graded (FG) nanobeams. The elastic properties of FG material vary continuously by gradually changing the volume fraction of the constituent materials in the thickness direction. Closed-form analytical solutions are obtained by using Navier’s solution technique. Non-dimensional displacements, stresses, natural frequencies and critical buckling loads for FG nanobeams are presented. The numerical results presented in this study can be served as a benchmark for future research.

Nonlinear Thermal Buckling Analysis of FGM Shallow Arches Under Linear Temperature Gradient

2014 ◽  
Author(s):  
H. Asgari ◽  
M. R. Eslami
Keyword(s):  
Temperature Gradient ◽  
Power Law ◽  
Material Properties ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Linear Temperature ◽  
Shallow Arches ◽  
Linear Temperature Gradient ◽  
Non Linear

In this study non-linear thermal buckling of circular shallow arches made of functionally graded materials subjected to a linear temperature gradient is investigated. For this purpose, a functionally graded circular shallow arch is considered that its strain-displacement relation follows the Donnells nonlinear shallow shell theory. The material properties are varied smoothly through the arch thickness according to the power law distribution of the volume fraction of constituent materials. Also, material properties are considered temperature-dependent. The classical single layer theory assumptions that are reasonable for slender arches are implemented. To investigate the large deformations of such arch, the von-Karman type geometrical nonlinearity is utilized that is suitable for moderately large class of rotations. The virtual displacement principle and calculus of variation are employed to derive the governing equilibrium equations and complete set of boundary conditions of the FGM arch. The adjacent equilibrium criterion is employed for the stability analysis of the FGM arch. An analytical approach is accomplished and a closed-forms solution for thermal bifurcation points of the FGM shallow arches is presented. Also critical bifurcation loads corresponding to the critical temperatures with the presence of non-linear pre-buckling deformations is obtained. Illustrative results examine the effect of various involved parameters such as power law index, opening angle, geometric parameter (or otherwise length to thickness ratio). Obtained numerical results represent that, in most cases, thermal bifurcation for the FGM arches occurs in the high temperatures and the critical buckling temperatures are approximately high even for slender FGM arches. Also effective of ceramic or metal rich area at the bottom surface of the FGM arch is investigated and results are presented for both cases and are compared together. Varieties between this two cases due to contrast between material and structural stretching-bending coupling effect. Results presented illustrative the ceramic rich area at the bottom surface cause the higher critical buckling temperatures for the FGM arches.

scholarly journals Parametric Study on Vibration and Harmonic Analysis of Moderately Thick Functionally Graded Plates Using FEM

2018 ◽  
Vol 237 ◽  
pp. 01007
Author(s):  
Avadesh K. Sharma ◽  
M K Gaur ◽  
R K Dwivedi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Harmonic Analysis ◽  
Material Properties ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Functionally Graded Plates ◽  
Power Law Distribution ◽  
Finite Element Package

Finite element method is used to investigate the free vibration and harmonic analysis of functionally graded plates. The material properties of the plates are assumed to vary continuously through their thickness direction according to a power-law distribution of the volume fractions of the plate constituents. The four noded shell 181 elements are used to analyse the functionally graded plates. The aim is to fill the void in the available literature with respect to the free vibration results of Functionally Graded plates. Convergence and Comparison studies with respect to the number of nodes has been carried out using FEM. The natural frequency, mode shape and harmonic analysis of FG plate has been determined using finite element package ANSYS.

scholarly journals Free Vibration Analysis of Simply Supported P-FGM Nanoplate Using a Nonlocal Four Variables Shear Deformation Plate Theory

2019 ◽  
Vol 69 (4) ◽  
pp. 9-24 ◽  
Author(s):  
Chikh Abdelbaki
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Power Law ◽  
Material Properties ◽  
Scale Effects ◽  
Plate Theory ◽  
Functionally Graded ◽  
Small Scale ◽  
Simply Supported ◽  
Shear Deformation Plate Theory

AbstractThis paper shows an analysis of the free vibration of functionally graded simply supported nanoplate. The nonlocal four variables shear deformation plate theory is used to predict the free vibration frequencies of functionally graded nanoplate simply supported using non-local elasticity theory with the introduction of small-scale effects. The effect of the material properties, thickness-length ratio, aspect ratio, the exponent of the power law, the vibration mode is presented, the current solutions are compared to those obtained by other researchers. Equilibrium equations are obtained using the virtual displacements principle. P-FGM Power law is used to have a distribution of material properties that vary across the thickness. The results are in good agreement with those of the literature.

scholarly journals Vibration analysis of rotating porous functionally graded material beams using exact formulation

2021 ◽  
pp. 107754632110278
Author(s):  
Mohammadreza Amoozgar ◽  
Len Gelman
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Material Properties ◽  
Functionally Graded ◽  
Distribution Model ◽  
Power Law Distribution ◽  
Cross Sectional ◽  
Rotating Speed ◽  
Rotating Blade ◽  
Graded Material

In this article, the exact free vibration of porous functionally graded rotating blades is investigated. The nonlinear 3D dynamics of the blade is simulated using the geometrically exact fully intrinsic beam equations, and the corresponding cross-sectional properties of the FG beam are developed. The material properties of the functionally graded material blade are graded through the thickness using a power law distribution. Furthermore, it is assumed that due to the manufacturing process, a level of porosity exists in the material which in turn can affect the material properties of the blade. Two porosity models resembling the even and uneven distributions of porosity are considered. First, the obtained results for a functionally graded material rotating blade are compared with those reported in the literature, and a very good agreement is observed. Furthermore, the effect of various parameters on the vibration of the functionally graded material beam is investigated. It is obtained that the dynamics of the rotating blade is sensitive to the type of the porosity due to manufacturing flaws. Moreover, the numerical results show that the blade length to height ratio, power law index, rotating speed and porosity distribution model affect the dynamics of the beam significantly.

Thermoelastic Response of FGM Plates with Temperature-Dependent Properties Resting on Variable Elastic Foundations

2015 ◽  
Vol 07 (06) ◽  
pp. 1550082 ◽  
Author(s):  
Mohammed Sobhy
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Power Law ◽  
Material Properties ◽  
Plate Theory ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Temperature Dependent ◽  
Simply Supported ◽  
Elastic Foundations

This paper deals with thermomechanical bending of functionally graded material (FGM) plates under various boundary conditions and resting on two-layer elastic foundations. One of these layers is Winkler springs with a variable modulus while the other is considered as a shear layer with a constant modulus. The plates are considered of the type having two opposite sides simply-supported, and the two other sides having combinations of simply-supported, clamped, and free boundary conditions. The temperature is obtained by solving the one-dimensional equation of heat conduction. The material properties of the plate are assumed to be graded continuously across the panel thickness. A simple power-law distribution in terms of the volume fractions of the constituents is used for estimating the effective material properties such as temperature-dependent thermoelastic properties. The governing equations are derived based on the sinusoidal shear deformation plate theory including the external load and thermal effects. The results of this theory are compared with those of other shear deformation theories. Various numerical results including the effect of boundary conditions, power-law index, plate aspect ratio, temperature difference, elastic foundation parameters, and side-to-thickness ratio on the bending of FGM plates are presented.

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