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.

scholarly journals Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Zakaria Ibnorachid ◽  
Lhoucine Boutahar ◽  
Khalid EL Bikri ◽  
Rhali Benamar
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Slenderness Ratio ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement

In this paper, free vibrations of Porous Functionally Graded Beams (P-FGBs), resting on two-parameter elastic foundations, and exposed to three forms of thermal field, uniform, linear, and sinusoidal, are studied using a Refined Higher-order shear Deformation Theory. The present theory accounts for shear deformation by considering a constant transverse displacement and a higher-order variation of the axial displacement through the thickness of the beam. The stress-free boundary conditions are satisfied on the upper and lower surfaces of the beam without using any shear correction factor. The material properties are temperature-dependent and vary continuously through the depth direction of the beam, based on a modified power-law rule, in which two kinds of porosity distributions, uniform, and nonuniform, through the cross-section area of the beam, are considered. Hamilton’s principle is applied to obtain governing equations of motion, which are solved using a Navier-type analytical solution for simply supported P-FGB. Numerical examples are proposed and discussed in detail, to prove the effect of the thermal environment, the porosity distribution, and the influence of several parameters such as the power-law index, porosity volume fraction, slenderness ratio, and elastic foundation parameters on the critical buckling temperatures and the natural frequencies of the P-FGB.

BI-STABLE ANALYSES OF LAMINATED FGM SHELLS

2012 ◽  
Vol 12 (02) ◽  
pp. 311-335 ◽  
Author(s):  
X. Q. HE ◽  
L. LI ◽  
S. KITIPORNCHAI ◽  
C. M. WANG ◽  
H. P. ZHU
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Optimum Combination ◽  
Thickness Direction ◽  
Power Law Distribution ◽  
Deployable Structures ◽  
Graded Material ◽  
Two Parameter

Based on an inextensional two-parameter analytical model for cylindrical shells, bi-stable analyses were carried out on laminated functionally graded material (FGM) shells with various layups of fibers. Properties of FGM shells are functionally graded in the thickness direction according to a volume fraction power law distribution. The effects of constituent volume fractions of FGM matrix are examined on the curvature and twist of laminated FGM shells. The results reveal that the optimum combination of constituents of FGM matrix can be obtained for the maximum twist of FGM shells with antisymmetric layups, which helps the design of deployable structures. The effects of Young's modulus of fibers and the symmetry of layups on bi-stable behaviors are also discussed in detail.

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.

Effect of In-Plane Load and Thermal Environment on Buckling and Vibration Behavior of Two-Dimensional Functionally Graded Tapered Timoshenko Nanobeam

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Roshan Lal ◽  
Chinika Dangi
Keyword(s):  
Thermal Environment ◽  
Slenderness Ratio ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Power Law Distribution ◽  
Energy Principle

Abstract In this work, buckling and vibration characteristics of two-dimensional functionally graded (FG) nanobeam of nonuniform thickness subjected to in-plane and thermal loads have been analyzed within the frame work of Timoshenko beam theory. The beam is tapered by linear variation in thickness along the length. The temperature-dependent material properties of the beam are varying along thickness and length as per a power-law distribution and exponential function, respectively. The analysis has been presented using Eringen’s nonlocal theory to incorporate the size effect. Hamilton’s energy principle has been used to formulate the governing equations of motion. These resulting equations have been solved via generalized differential quadrature method (GDQM) for three combinations of clamped and simply supported boundary conditions. The effect of in-plane load together with temperature variation, nonuniformity parameter, gradient indices, nonlocal parameter, and slenderness ratio on the natural frequencies is illustrated for the first three modes of vibration. The critical buckling loads in compression have been computed by putting the frequencies equal to zero. A significant contribution of in-plane load on mechanical behavior of two-directional functionally graded nanobeam with nonuniform cross section has been noticed. Results are in good accordance.

Electro-magnetic effects on nonlocal dynamic behavior of embedded piezoelectric nanoscale beams

2017 ◽  
Vol 28 (15) ◽  
pp. 2007-2022 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati
Keyword(s):  
Elastic Foundation ◽  
Power Law ◽  
Slenderness Ratio ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Electric Voltage ◽  
Electro Magnetic ◽  
Functionally Graded Nanobeam

This article investigates vibration behavior of magneto-electro-elastic functionally graded nanobeams embedded in two-parameter elastic foundation using a third-order parabolic shear deformation beam theory. Material properties of magneto-electro-elastic functionally graded nanobeam are supposed to be variable throughout the thickness based on power-law model. Based on Eringen’s nonlocal elasticity theory which captures the small size effects and using Hamilton’s principle, the nonlocal governing equations of motions are derived and then solved analytically. Then, the influences of elastic foundation, magnetic potential, external electric voltage, nonlocal parameter, power-law index, and slenderness ratio on the frequencies of the embedded magneto-electro-elastic functionally graded nanobeams are studied.

Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment

2016 ◽  
Vol 24 (3) ◽  
pp. 549-564 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati
Keyword(s):  
Power Law ◽  
Natural Frequencies ◽  
Thermal Environment ◽  
Slenderness Ratio ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Temperature Fields ◽  
Electric Voltage ◽  
Fg Nanobeam

In this paper, vibration characteristics of magneto-electro-thermo-elastic functionally graded (METE-FG) nanobeams is investigated in the framework of third order shear deformation theory. Magneto-electro-thermo-elastic properties of FG nanobeam are supposed to vary smoothly and continuously along the thickness based on power-law form. To capture the small size effects, Eringen’s nonlocal elasticity theory is adopted. By using the Hamilton’s principle, the nonlocal governing equations are derived and then solved analytically to obtain the natural frequencies of METE-FG nanobeams. The reliability of proposed model and analytical method in predicting natural frequencies of METE-FG nanobeam is evaluated with comparison to some cases in the literature. Numerical results are provided indicating the influences of several parameters including magnetic potential, external electric voltage, temperature fields, power-law exponent, nonlocal parameter and slenderness ratio on the frequencies of METE-FG nanobeams. It is found that the vibrational behavior of METE-FG nanobeams is significantly impressed by these effects.

scholarly journals Optimum response of functionally graded piezoelectric plates in thermal environments

2017 ◽  
Vol 35 (3) ◽  
pp. 606-617 ◽  
Author(s):  
Hossein Nourmohammadi ◽  
Bashir Behjat
Keyword(s):  
Power Law ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Plate Theory ◽  
Poisson Ratio ◽  
Functionally Graded ◽  
Sensors And Actuators ◽  
Thermal Environments ◽  
Functionally Graded Piezoelectric ◽  
Power Law Index

AbstractIn this article, the static response of the functionally graded piezoelectric (FGP) plates with piezoelectric layers (sandwich FGPM) is studied based on the first order shear deformation plate theory. The plate is under mechanical, electrical and thermal loadings and finite element method is employed to obtain the solution of the equation. All mechanical, thermal and piezoelectric properties, except Poisson ratio, obey the power law distribution through the thickness. By solving the governing equation, optimum value of power law index is investigated in each type of loading. The effects of different volume fraction index, layer arrangements, various boundary conditions and different loading types, are studied on the deflection of FGPM plate. It is inferred that, the correlations between the deflection, power law index and layer arrangement are completely different in the mechanical and thermal loading and the optimum value of the power law index should be selected in each case separately. This optimum values can be used as a design criterion to build a reliable sensors and actuators in thermal environments.

Thermal Buckling and Postbuckling Analysis of Functionally Graded Concrete Slabs with Initial Imperfections

2018 ◽  
Vol 18 (11) ◽  
pp. 1850142 ◽  
Author(s):  
Huanqing Zhang ◽  
Zheng Zhang ◽  
Helong Wu ◽  
Sritawat Kitipornchai ◽  
Guozhong Chai ◽  
...  
Keyword(s):  
Volume Fraction ◽  
Concrete Slab ◽  
Slenderness Ratio ◽  
Initial Imperfection ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Fiber Reinforced Concrete ◽  
Fe Model ◽  
Concrete Layer ◽  
Thick Layers

This paper proposes a novel functionally graded (FG) concrete slab and investigates its thermal buckling and postbuckling performance using the finite-element (FE) method. The concrete slab consists of three homogeneous thick layers — a fiber-reinforced concrete layer, a geopolymer concrete layer, and a plain Portland cement (PPC) layer — with a thin FG layer between the thick layers. The mechanical properties of the thin FG layers are exponentially graded across the thickness direction. The effects of initial imperfection, the self-weight of the slab, and the friction between the slab and rigid foundation are considered in the analysis. The FE model is validated against the results reported in the literature. A comprehensive parametric study is conducted to examine the effects of the thickness and volume fraction index of the FG layer, initial imperfection, self-weight, friction, and slab slenderness ratio on the thermal buckling and postbuckling behaviors of the concrete slab. The numerical results demonstrate that the proposed FG slab exhibits remarkably better buckling and postbuckling resistance than a conventional PPC concrete slab and that the influences of both self-weight and friction are important and cannot be neglected.

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