Non-linear thermo-mechanical cylindrical bending of functionally graded plates

2008 ◽  
Vol 222 (3) ◽  
pp. 305-318 ◽  
Author(s):  
F Fallah ◽  
A Nosier
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Cylindrical Bending ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Fg Plates ◽  
Non Linear ◽  
The One

Based on the first-order non-linear von Karman theory, cylindrical bending of functionally graded (FG) plates subjected to mechanical, thermal, and combined thermo-mechanical loadings are investigated. Analytical solutions are obtained for an FG plate with various clamped and simply-supported boundary conditions. The closed form solutions obtained are very simple to be used in design purposes. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. The effects of non-linearity, material property, and boundary conditions on various response quantities are studied and discussed. It is found that linear analysis is inadequate for analysis of simply-supported FG plates even in the small deflection range especially when thermal load is present. Also it is shown that bending—extension coupling can not be seen in response quantities of clamped FG plates. Also an exact solution is developed for the one-dimensional heat conduction equation with variable heat conductivity coefficient.

Static Analysis of Moderately Thick Functionally Graded Plates With Various Boundary Conditions

2010 ◽  
Author(s):  
Nastaran Shahmansouri ◽  
Mohammad Mohammadi Aghdam ◽  
Kasra Bigdeli
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Various Boundary Conditions ◽  
Fg Plates ◽  
Ode Systems

The present study investigates static analyses of moderately thick FG plates. Using the First Order Shear Deformation Theory (FSDT), functionally graded plates subjected to transversely distributed loading with various boundary conditions are studied. Effective mechanical properties which vary from one surface of the plate to the other assumed to be defined by a power law form of distribution. Different ceramic-metal sets of materials are studied. Solution of the governing equations, including five equilibrium and eight constitutive equations, is obtained by the Extended Kantorovich Method (EKM). The system of thirteen Partial Differential Equations (PDEs) in terms of displacements, rotations, force and moment resultants are considered as multiplications of separable function of independent variables x and y. Then by successful utilization of the EKM these equations are converted to a double set of ODE systems in terms of x and y. The obtained ODE systems are then solved iteratively until final convergence is achieved. Closed form solution is presented for these ODE sets. It is shown that the method is very stable and provides fast convergence and highly accurate predictions for both thin and moderately thick plates. Comparison of the normal stresses at various points of rectangular plates and deflection of mid-point of the plate are presented and compared with available data in the literature. The effects of the volume fraction exponent n on the behavior of the normalized deflection, moment resultants and stresses of FG plates are also studied. To validate data for analysis fully clamped FG plates, another analysis was carried out using finite element code ANSYS. Close agreement is observed between predictions of the EKM and ANSYS.

Free vibration problem of embedded magneto-electro-thermo-elastic nanoplate made of functionally graded materials via nonlocal third-order shear deformation theory

2017 ◽  
Vol 29 (5) ◽  
pp. 741-763 ◽  
Author(s):  
Ali Kiani ◽  
Moslem Sheikhkhoshkar ◽  
Ali Jamalpoor ◽  
Mostafa Khanzadi
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Nonlocal Parameter ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Graded Materials ◽  
Simply Supported

In the present article, according to the nonlocal elasticity theory within the framework of the third-order shear deformable plate assumption, the theoretical analysis of thermomechanical vibration response of magneto-electro-thermo-elastic nanoplate made of functionally graded materials resting on the visco-Pasternak medium is carried out. The simply supported magneto-electro-thermo-elastic nanoplate is supposed to subject to initial external electric, magnetic potentials, and temperature environment. The material characteristics of magneto-electro-thermo-elastic nanoplate are assumed to be variable continuously across the thickness direction based upon power law distribution. Hamilton’s principle is utilized to achieve the partial differential equations and corresponding boundary conditions. The equilibrium equations are solved analytically to determine the complex eigenfrequency using Navier’s approach which satisfies the simply supported boundary conditions. Numerical studies are performed to illustrate the dependency of the natural frequency of the system on the damping coefficient of the visco-Pasternak medium, nonlocal parameter, aspect ratio, temperature change, volume fraction index of functionally graded material, initial external electric voltage, initial external magnetic potential, and plate thickness. It is clearly indicated that these factors have highly significant impacts on the dynamic behavior of the proposed system.

scholarly journals Non-Linear Stability of the Step-Variable In-Plane Functionally Graded Plates Subjected to Linear Approaches of the Edges

Materials ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 1439
Author(s):  
Zbigniew Kołakowski ◽  
Leszek Czechowski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Linear Stability ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Simply Supported ◽  
Fg Plates ◽  
Non Linear ◽  
The Stability ◽  
Material Gradation

The analysis of gradations through the thickness in structures are commonly used. It usually refers to the problems of the stability of functionally graded (FG) structures. In this work, rectangular in-plane FG plates built of a material gradation along the transversal direction were assumed. Five-strip FG plates with four cases that were based on the boundary conditions on longitudinal edges and simply supported on transverse loaded edges were considered. The non-linear stability problems of the FG plates that were subjected to linear approaches of the transverse edges for several types of loads were solved. The estimations were executed with two methods: an analytical-numerical way based on Koiter’s theory and finite element method (FEM).

Free vibration analysis of functionally graded thin annular sector plates using the differential quadrature method

2010 ◽  
Vol 225 (3) ◽  
pp. 568-583 ◽  
Author(s):  
S H Mirtalaie ◽  
M A Hajabasi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Fg Plates ◽  
Annular Sector

In this article, the differential quadrature method (DQM) is used to study the free vibration of functionally graded (FG) thin annular sector plates. The material properties of the FG-plate are assumed to vary continuously through the thickness, according to the power-law distribution. The governing differential equations of motion are derived based on the classical plate theory and solved numerically using DQM. The natural frequencies of thin FG annular sector plates under various combinations of clamped, free, and simply supported boundary conditions are presented for the first time. To ensure the accuracy of the method, the natural frequencies of a pure metallic plate are calculated and compared with those existing in the literature for the homogeneous plate. In this case, the result shows very good agreement. For the FG-plates, the effects of boundary conditions, volume fraction exponent, and variation of Poisson's ratio on the free vibrational behaviour of the plate are studied.

A New Trigonometric Higher-Order Shear and Normal Deformation Theory for Functionally Graded Plates

2016 ◽  
Author(s):  
Ankit Gupta ◽  
Mohammad Talha
Keyword(s):  
Boundary Conditions ◽  
Deformation Theory ◽  
Volume Fraction ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Functionally Graded Plates ◽  
Power Law Distribution ◽  
Normal Deformation ◽  
3 Dimensional

In the present study, a new trigonometric higher-order shear and normal deformation theory is proposed and implemented to investigate the free vibration characteristics of functionally graded material (FGM) plates. The present theory comprises the nonlinear variation in the in-plane and transverse displacement and accommodates, both shear deformation and thickness stretching effects. It also satisfies the stress-free boundary conditions on the top and bottom surfaces of the plate without requiring any shear correction factor. The governing equations are derived using the variational principle. The effective mechanical properties of FGM plates are assumed to vary according to a power law distribution of the volume fraction of the constituents. Poisson’s ratios of FGM plates are assumed constant. The numerical solution has been obtained using an efficient displacement based C0 finite element model with eight degrees of freedom per node. The computed results are compared with 3-dimensional and quasi-3-dimensional solutions and those projected by other well-known plate theories. Natural frequencies of the functionally graded plates with various side-to-thickness ratios, boundary conditions, and volume fraction index ‘n’ have been computed. It can be concluded that the proposed model is not only accurate but also simple in predicting the vibration behavior of functionally graded plates.

Free Vibration Analysis of Functionally Graded Plates on Two-Parameter Elastic Supports and in Contact With Stationary Fluid

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Arash Shahbaztabar ◽  
Ahmad Rahbar Ranji
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Volume Fraction ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Power Law Distribution ◽  
Fg Plates ◽  
The Impact ◽  
Two Parameter

Free vibration analysis of functionally graded (FG) rectangular plates on two-parameter elastic foundation and vertically coupled with fluid is the objective of this work. The fluid domain is considered to be infinite in length, but it is bounded in depth and width directions, and the effects of hydrostatic pressure and free surface waves are not taken into account. The mechanical properties of the FG plates are assumed to vary continuously through the thickness direction according to a power-law distribution of the volume fraction of the constituents. The accuracy and applicability of the formulation is illustrated by comparison studies with those reported in the open literature. At the end, parametric studies are carried out to examine the impact of different parameters on the natural frequencies.

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.

A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges

2010 ◽  
Vol 224 (9) ◽  
pp. 1831-1841 ◽  
Author(s):  
M Mohammadi ◽  
A R Saidi ◽  
E Jomehzadeh
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Fg Plates

In this article, a novel analytical method for decoupling the coupled stability equations of functionally graded (FG) rectangular plates is introduced. Based on the Mindlin plate theory, the governing stability equations that are coupled in terms of displacement components are derived. Introducing four new functions, the coupled stability equations are converted into two independent equations. The obtained equations have been solved for buckling analysis of rectangular plates with simply-supported two edges and arbitrary boundary conditions along the other edges (Levy boundary conditions). The critical buckling loads are presented for different loading conditions, various thickness to side and aspect ratios, some powers of FG materials, and various boundary conditions. The presented results for buckling of moderately thick FG plates with two simply-supported edges are reported for the first time.

scholarly journals Hydro-elastic vibration analysis of functionally graded rectangular plate in contact with stationary fluid

2018 ◽  
Author(s):  
Shahrouz Yousefzadeh ◽  
Ashkan Akbari ◽  
Mohammad Najafi
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Volume Fraction ◽  
Applied Pressure ◽  
Plate Boundary ◽  
Shear Deformation Theory ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Power Law Distribution

This study investigates the free vibration of a moderately thick rectangular plate, which is composed of functionally graded materials and floating on incompressible fluid. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fraction of the constituent. The governing equations of the plate are analytically derived based on the first-order shear deformation theory with consideration of rotational inertial effects and transverse shear stresses. Applied pressure on the free surface of the plate is obtained by the velocity potential function together with Bernoulli’s equation. The equation governing on the oscillatory behaviour of the fluid is obtained by solving Laplace equation with satisfying the boundary conditions. The natural frequencies and shape modes of the rectangular plate are determined by decoupling and solving the motion equations system. Then, analyses of the numerical results of free vibrations and the effects of the different parameters such as thickness to length of the plate, boundary conditions, fluid density, index of volume fraction and the height of the fluid on the frequencies are investigated. Finally, the results of this research in limit case is compared and validated with the results of other researchers and finite element model.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

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