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.

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 Static analysis of four-parameter functionally graded plates with general boundary conditions

2019 ◽  
Vol 13 (2) ◽  
pp. 12-23
Author(s):  
Hoang Thu Phuong ◽  
Tran Huu Quoc ◽  
Ho Thi Hien
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Material Properties ◽  
Load Distribution ◽  
Plate Theory ◽  
Ritz Method ◽  
Functionally Graded ◽  
General Boundary ◽  
Geometrical Parameters ◽  
General Boundary Conditions

In this study, the Ritz variational method is used to analyze and solve the bending problem of rectangular functionally graded material plate with general boundary conditions and subject to some types of load distribution over the entire plate domain. Based on the Kirchoff plate theory, the equilibrium equations are obtained by minimizing the total potential energy. The material properties are assumed to be graded through the thickness of the plates according to a power law with four parameters. The accuracy of the solution has been checked and validated through different comparisons to that available literature. A wide variety of examples have been carried out to reveal the influences of different geometrical parameters, FGM power law index, type of load distribution and boundary conditions on the bending responses of the plates. The results show that the gradients in material properties play an important role in determining the response of the FGM plates.Keywords: FGM; Kirchhoff plate; Ritz method; boundary conditions.

Thermomechanical postbuckling analysis of eccentrically stiffened FGM sandwich plates with general Sigmoid and power laws based on TSDT

2016 ◽  
Vol 20 (8) ◽  
pp. 907-945 ◽  
Author(s):  
Dao Van Dung ◽  
Nguyen Thi Nga
Keyword(s):  
Shear Deformation ◽  
Material Properties ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Power Laws ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Temperature Dependent ◽  
Third Order ◽  
Shear Deformation Plate Theory

The buckling and postbuckling behaviors of eccentrically stiffened sandwich plates on elastic foundations subjected to in-plane compressive loads, thermal loads, or thermomechanical loads are presented analytically by using the Reddy’s third-order shear deformation plate theory with von Karman geometrical nonlinearity. Four cases of general Sigmoid and power laws are considered. The material properties of the facesheets, the core layer, and stiffeners are assumed to be temperature-dependent. Theoretical formulations based on the smeared stiffeners technique and third-order shear deformation plate theory are derived. The expressions of thermal parameters are found in the analytical form. Applying the Galerkin method, the expressions for determination of the critical buckling load and analysis of the postbuckling mechanical and thermal load–deflection curves are obtained. The iterative algorithm is presented for the case of temperature-dependent plate material properties. In addition, the influences of thermal element, functionally graded material stiffeners, the facesheet thickness to total thickness ratio, initial imperfection, and foundations are clarified in detail.

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.

scholarly journals A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities

2016 ◽  
Vol 2016 ◽  
pp. 1-20 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Ali Jafari
Keyword(s):  
Differential Equations ◽  
Porous Material ◽  
Power Law ◽  
Material Properties ◽  
Solution Method ◽  
Equations Of Motion ◽  
Higher Order ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Temperature Dependent

In the present paper, thermomechanical vibration characteristics of functionally graded (FG) Reddy beams made of porous material subjected to various thermal loadings are investigated by utilizing a Navier solution method for the first time. Four types of thermal loadings, namely, uniform, linear, nonlinear, and sinusoidal temperature rises, through the thickness direction are considered. Thermomechanical material properties of FG beam are assumed to be temperature-dependent and supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM) which is modified to approximate the porous material properties with even and uneven distributions of porosities phases. The governing differential equations of motion are derived based on higher order shear deformation beam theory. Hamilton’s principle is applied to obtain the governing differential equations of motion which are solved by employing an analytical technique called the Navier type solution method. Influences of several important parameters such as power-law exponents, porosity distributions, porosity volume fractions, thermal effects, and slenderness ratios on natural frequencies of the temperature-dependent FG beams with porosities are investigated and discussed in detail. It is concluded that these effects play significant role in the thermodynamic behavior of porous FG beams.

Hypersonic Flutter Analysis of Functionally Graded Panels under Thermal and Aerodynamic Loads

2009 ◽  
Vol 631-632 ◽  
pp. 41-46
Author(s):  
Sun Bae Kim ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Virtual Work ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Aerodynamic Loads ◽  
Linear Rule ◽  
Structural Nonlinearity ◽  
Post Buckling

In this work, hypersonic aero-thermo post-buckling and thermal flutter behaviors of Functionally Graded (FG) panels under thermal and aerodynamic loads are investigated. The volume fractions of constitutive materials of the panels are gradually varied from ceramic to metal in the thickness direction based on a simple power law distribution. Thus, the material properties of the panel are also changed by a linear rule of mixture. Furthermore, the material properties are assumed to be temperature dependent because the panels are mainly used in the high temperature environments. Using the principle of virtual work, the equations of motion of the first-order shear deformation plate theory (FSDPT) are derived and the finite element method is applied to get the solution. In the formulation, the von Karman strain-displacement relationship is used for structural nonlinearity, and the partial second-order piston theory is adopted to consider the aerodynamic nonlinearity. Newton-Raphson iterative technique is used to solve the governing equations, and linear eigenvalue analysis is performed to obtain the hypersonic flutter boundaries.

scholarly journals Strong and Weak Formulations of a Mixed Higher-Order Shear Deformation Theory for the Static Analysis of Functionally Graded Beams under Thermo-Mechanical Loads

2020 ◽  
Vol 4 (4) ◽  
pp. 158 ◽  
Author(s):  
Chih-Ping Wu ◽  
Zhan-Rong Xu
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Static Analysis ◽  
Material Properties ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Mechanical Loads ◽  
Effective Material Properties ◽  
Fg Beam

The strong and weak formulations of a mixed layer-wise (LW) higher-order shear deformation theory (HSDT) are developed for the static analysis of functionally graded (FG) beams under various boundary conditions subjected to thermo-mechanical loads. The material properties of the FG beam are assumed to obey a power-law distribution of the volume fractions of the constituents through the thickness of the FG beam, for which the effective material properties are estimated using the rule of mixtures, or it is directly assumed that the effective material properties of the FG beam obey an exponential function distribution along the thickness direction of the FG beam. The results shown in the numerical examples indicate that the mixed LW HSDT solutions for elastic and thermal field variables are in excellent agreement with the accurate solutions available in the literature. A parametric study related to various effects on the coupled thermo-mechanical behavior of FG beams is carried out, including the aspect ratio, the material-property gradient index, and different boundary conditions.

scholarly journals Thermo-mechanical contact problems and elastic behaviour of single and double sides functionally graded brake disks with temperature-dependent material properties

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Mehdi Bayat ◽  
Ibrahim M. Alarifi ◽  
Ali Akbar Khalili ◽  
Tarek M. A. A. El-Bagory ◽  
Hoang Minh Nguyen ◽  
...  
Keyword(s):  
Material Properties ◽  
Radial Strain ◽  
Functionally Graded ◽  
Elastic Behaviour ◽  
Contact Friction ◽  
Vertical Force ◽  
Brake Pad ◽  
Power Law Distribution ◽  
Temperature Dependent ◽  
Brake Disk

Abstract A thermo-elastic contact problem of functionally graded materials (FGMs) rotating brake disk with different pure brake pad areas under temperature dependent material properties is solved by Finite Element Method (FEM). The properties of brake disk change gradually from metal to ceramic by power-law distribution along the radial direction from the inner to the outer surface. Areas of the pure pad are changing while the vertical force is constant. The ratio of brake pad thickness to FGMs brake disk thickness is assumed 0.66. Two sources of thermal loads are considered: (1) Heat generation between the pad and brake disk due to contact friction, and (2) External thermal load due to a constant temperature at inner and outer surfaces. Mechanical responses of FGMs disk are compared with several pad contact areas. The results for temperature-dependent and temperature-independent material properties are investigated and presented. The results show that the absolute value of the shear stress in temperature-dependent material can be greater than that for temperature-independent material. The radial stress for some specific grading index (n = 1.5) is compressive near the inner surface for double contact while it is tensile for a single contact. It is concluded that the radial strain for some specific value of grading index (n = 1) is lower than other FGMs and pure double side contact brake disks.

Effect of Winkler and Pasternak elastic foundation on the vibration of rotating functionally graded material cylindrical shell

2018 ◽  
Vol 232 (24) ◽  
pp. 4564-4577 ◽  
Author(s):  
Muzamal Hussain ◽  
Muhammad Nawaz Naeem ◽  
Mohammad Reza Isvandzibaei
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Radius Ratio ◽  
Wave Number ◽  
Simply Supported ◽  
Elastic Foundations

In this paper, vibration characteristics of rotating functionally graded cylindrical shell resting on Winkler and Pasternak elastic foundations have been investigated. These shells are fabricated from functionally graded materials. Shell dynamical equations are derived by using the Hamilton variational principle and the Langrangian functional framed from the shell strain and kinetic energy expressions. Elastic foundations, namely Winkler and Pasternak moduli are inducted in the tangential direction of the shell. The rotational motions of the shells are due to the Coriolis and centrifugal acceleration as well as the hoop tension produced in the rotating case. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in rotating functionally graded cylindrical shell. The complex exponential functions, with the axial modal numbers that depend on the boundary conditions stated at edges of a cylindrical shell, have been used to compute the axial modal dependence. In our new investigation, frequency spectra are obtained for circumferential wave number, length-to-radius ratio, height-to-radius ratio with simply supported–simply supported and clamped–clamped boundary conditions without elastic foundation. Also, the effect of elastic foundation on the rotating cylindrical shells is examined with the simply supported–simply supported edge. To check the validity of the present method, the fundamental natural frequencies of non-rotating isotropic and functionally graded cylindrical shells are compared with the open literature. Also, a comparison is made for infinitely long rotating with the earlier published paper.

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