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.

scholarly journals Buckling Analysis of Smart Size-Dependent Higher Order Magneto-Electro-Thermo-Elastic Functionally Graded Nanosize Beams

2016 ◽  
Vol 33 (1) ◽  
pp. 23-33 ◽  
Author(s):  
F. Ebrahimi ◽  
M. R. Barati
Keyword(s):  
Power Law ◽  
Thermal Loading ◽  
Slenderness Ratio ◽  
Nonlocal Parameter ◽  
Higher Order ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Beam Model ◽  
Thickness Direction ◽  
Power Law Distribution

AbstractThe present paper examines the thermal buckling of nonlocal magneto-electro-thermo-elastic functionally graded (METE-FG) beams under various types of thermal loading namely uniform, linear and sinusoidal temperature rise and also heat conduction. The material properties of nanobeam are graded in the thickness direction according to the power-law distribution. Based on a higher order beam theory as well as Hamilton's principle, nonlocal governing equations for METE-FG nanobeam are derived and are solved using Navier type method. The small size effect is captured using Eringen's nonlocal elasticity theory. The most beneficial feature of the present beam model is to provide a parabolic variation of the transverse shear strains across the thickness direction and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. Various numerical examples are presented investigating the influences of thermo-mechanical loadings, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on thermal buckling behavior of nanobeams made of METE-FG materials.

Analysis of sandwich Timoshenko porous beam with temperature-dependent material properties: Magneto-electro-elastic vibration and buckling solution

2019 ◽  
Vol 25 (23-24) ◽  
pp. 2875-2893 ◽  
Author(s):  
M. Bamdad ◽  
M. Mohammadimehr ◽  
K. Alambeigi
Keyword(s):  
Timoshenko Beam ◽  
Material Properties ◽  
Vinylidene Fluoride ◽  
Equations Of Motion ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Distribution Patterns ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Temperature Dependent

Vibration and buckling analysis of a magneto-electro-elastic sandwich Timoshenko beam with a porous core and poly-vinylidene fluoride (PVDF) matrix reinforced by carbon nanotubes (CNTs) is considered as face layers and material properties of CNTs and PVDF are assumed to be temperature-dependent. Different CNT distribution patterns including uniform distribution, AV (which top and bottom face sheets have functionally graded-A (FG-A) and functionally graded-V (FG-V) CNT distribution patterns, respectively) and VA patterns are employed. The governing equations of motion are derived based on Timoshenko beam theory, and Navier's solution is used to solve these equations. The sandwich beam resting on a Pasternak foundation and face layers are subjected to electric and magnetic potentials. The effect of different parameters such as porosity coefficient, electric and magnetic potential, parameters of foundation, and geometrical parameters are investigated on vibration and buckling behavior of the sandwich beam. Numerical results of this paper show that porosity distribution has a significant effect on the stiffness of the sandwich beam. The results can be used for future analysis of magneto-electro-mechanical sandwich systems as actuators and sensors.

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.

Designing Optimal Volume Fractions For Functionally Graded Materials With Temperature-Dependent Material Properties

2006 ◽  
Vol 74 (5) ◽  
pp. 861-874 ◽  
Author(s):  
Florin Bobaru
Keyword(s):  
Functionally Graded Materials ◽  
Material Properties ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Dominant Factor ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Critical Stresses ◽  
Non Linear

We present a numerical approach for material optimization of metal-ceramic functionally graded materials (FGMs) with temperature-dependent material properties. We solve the non-linear heterogeneous thermoelasticity equations in 2D under plane strain conditions and consider examples in which the material composition varies along the radial direction of a hollow cylinder under thermomechanical loading. A space of shape-preserving splines is used to search for the optimal volume fraction function which minimizes stresses or minimizes mass under stress constraints. The control points (design variables) that define the volume fraction spline function are independent of the grid used in the numerical solution of the thermoelastic problem. We introduce new temperature-dependent objective functions and constraints. The rule of mixture and the modified Mori-Tanaka with the fuzzy inference scheme are used to compute effective properties for the material mixtures. The different micromechanics models lead to optimal solutions that are similar qualitatively. To compute the temperature-dependent critical stresses for the mixture, we use, for lack of experimental data, the rule-of-mixture. When a scalar stress measure is minimized, we obtain optimal volume fraction functions that feature multiple graded regions alternating with non-graded layers, or even non-monotonic profiles. The dominant factor for the existence of such local minimizers is the non-linear dependence of the critical stresses of the ceramic component on temperature. These results show that, in certain cases, using power-law type functions to represent the material gradation in FGMs is too restrictive.

Geometrically nonlinear dynamic response and vibration of shear deformable eccentrically stiffened functionally graded material cylindrical panels subjected to thermal, mechanical, and blast loads

2018 ◽  
Vol 22 (3) ◽  
pp. 658-688 ◽  
Author(s):  
Nguyen Dinh Duc ◽  
Ngo Duc Tuan ◽  
Pham Hong Cong ◽  
Ngo Dinh Dat ◽  
Nguyen Dinh Khoa
Keyword(s):  
Dynamic Response ◽  
Functionally Graded Material ◽  
Material Properties ◽  
Nonlinear Dynamic ◽  
Functionally Graded ◽  
Blast Loads ◽  
Temperature Dependent ◽  
Nonlinear Dynamic Response ◽  
Cylindrical Panels ◽  
Graded Material

Based on the first order shear deformation shell theory, this paper presents an analysis of the nonlinear dynamic response and vibration of imperfect eccentrically stiffened functionally graded material (ES-FGM) cylindrical panels subjected to mechanical, thermal, and blast loads resting on elastic foundations. The material properties are assumed to be temperature-dependent and graded in the thickness direction according to simple power-law distribution in terms of the volume fractions of the constituents. Both functionally graded material cylindrical panels and stiffeners having temperature-dependent properties are deformed under temperature, simultaneously. Numerical results for the dynamic response of the imperfect ES-FGM cylindrical panels with two cases of boundary conditions are obtained by the Galerkin method and fourth-order Runge–Kutta method. The results show the effects of geometrical parameters, material properties, imperfections, mechanical and blast loads, temperature, elastic foundations and boundary conditions on the nonlinear dynamic response of the imperfect ES-FGM cylindrical panels. The obtained numerical results are validated by comparing with other results reported in the open literature.

Temperature-Dependent Vibration of Various Types of Sandwich Beams with Porous FGM Layers

2020 ◽  
pp. 2150016
Author(s):  
Mohsen Rahmani ◽  
Sajjad Dehghanpour
Keyword(s):  
Thermal Stresses ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Type I ◽  
Sandwich Beams ◽  
Temperature Dependent ◽  
The Core ◽  
Graded Layers ◽  
Lagrange Strain

By using a high order sandwich beams theory which is modified by considering the transverse flexibility of the core, free vibration characteristics of two models of sandwich beams are studied in this paper. In type-I, functionally graded layers coat a homogeneous core, and in type-II, an FG core is covered by homogeneous face sheets. To increase the accuracy of the model of the FGM properties, even and uneven porosity distributions are applied, and all materials are considered temperature-dependent. Nonlinear Lagrange strain and thermal stresses of the face sheets and in-plane strain of the core are considered. To obtain the governing equations of motion, Hamilton’s principle is used and a Galerkin method is used to solve them for simply supported and clamped boundary conditions. To verify the results of this study, they are compared with the results of literatures. Also, the effect of variation of temperature, some geometrical parameters and porosities on the frequency are studied.

scholarly journals A state-based peridynamic formulation for functionally graded Kirchhoff plates

2020 ◽  
pp. 108128652096338
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Material Properties ◽  
Lagrange Equation ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Benchmark Problems ◽  
Transverse Loading ◽  
Stress Concentrations ◽  
Element Analysis ◽  
Kirchhoff Plates ◽  
Peridynamic Model

Functionally graded materials are a potential alternative to traditional fibre-reinforced composite materials as they have continuously varying material properties which do not cause stress concentrations. In this study, a state-based peridynamic model is presented for functionally graded Kirchhoff plates. Equations of motion of the new formulation are obtained using the Euler–Lagrange equation and Taylor’s expansion. The formulation is verified by considering several benchmark problems including a clamped plate subjected to transverse loading and a simply supported plate subjected to transverse loading and inclined loading. The material properties are chosen such that Young’s modulus is assumed to be varied linearly through the thickness direction and Poisson’s ratio is constant. Peridynamic results are compared against finite element analysis results, and a very good agreement is obtained between the two approaches.

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