Thermal Buckling Responses of a Graphene Reinforced Composite Micropanel Structure

2020 ◽  
Vol 12 (01) ◽  
pp. 2050010 ◽  
Author(s):  
H. Moayedi ◽  
H. Aliakbarlou ◽  
M. Jebeli ◽  
O. Noormohammadiarani ◽  
M. Habibi ◽  
...  
Keyword(s):  
Scale Effects ◽  
Differential Quadrature Method ◽  
Current Model ◽  
Thermal Buckling ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Reinforced Composite ◽  
Generalized Differential ◽  
Doubly Curved

This is the first research on the thermal buckling analysis of graphene nanoplatelets reinforced composite (GPLRC) doubly curved open cylindrical micropanel in the framework of numerical-based two-dimensional generalized differential quadrature method (2D-GDQM). Additionally, the small-scale effects are analyzed based on nonlocal strain gradient theory (NSGT). The stresses and strains are obtained using the high-order shear deformable theory (HOSDT). The rule of mixture is employed to obtain varying thermal expansion, and Poisson’s ratio, while module of elasticity is computed by modified Halpin–Tsai model. In addition, nonlinear temperature changes along the GPLRC micropanel’s thickness direction. Governing equations and boundary conditions of the GPLRC doubly curved open cylindrical micropanel are obtained by implementing the extended Hamilton’s principle. Besides, for the validation of the results, the results of current model are compared to the results acquired from analytical method. The results show that GPL weight function ([Formula: see text], the ratio of shell curvatures ([Formula: see text]/[Formula: see text], NSG parameters, and geometric parameters have a significant influence on the thermal buckling characteristics of the GPLRC doubly curved open cylindrical micropanel.

Mechanical Behavior of Functionally Graded Nano-Cylinders Under Radial Pressure Based on Strain Gradient Theory

2018 ◽  
Vol 35 (4) ◽  
pp. 441-454 ◽  
Author(s):  
M. Shishesaz ◽  
M. Hosseini
Keyword(s):  
Mechanical Behavior ◽  
Strain Gradient ◽  
Material Properties ◽  
Scale Effects ◽  
Radial Pressure ◽  
Functionally Graded ◽  
High Order ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory

ABSTRACTIn this paper, the mechanical behavior of a functionally graded nano-cylinder under a radial pressure is investigated. Strain gradient theory is used to include the small scale effects in this analysis. The variations in material properties along the thickness direction are included based on three different models. Due to slight variations in engineering materials, the Poisson’s ratio is assumed to be constant. The governing equation and its corresponding boundary conditions are obtained using Hamilton’s principle. Due to the complexity of the governed system of differential equations, numerical methods are employed to achieve a solution. The analysis is general and can be reduced to classical elasticity if the material length scale parameters are taken to be zero. The effect of material indexn, variations in material properties and the applied internal and external pressures on the total and high-order stresses, are well examined. For the cases in which the applied external pressure at the inside (or outside) radius is zero, due to small effects in nano-cylinder, some components of the high-order radial stresses do not vanish at the boundaries. Based on the results, the material inhomogeneity indexn, as well as the selected model through which the mechanical properties may vary along the thickness, have significant effects on the radial and circumferential stresses.

Small-Scale Effects on the Buckling of Skew Nanoplates Based on Non-Local Elasticity and Second-Order Strain Gradient Theory

2017 ◽  
Vol 34 (4) ◽  
pp. 443-452 ◽  
Author(s):  
B. Shahriari ◽  
S. Shirvani
Keyword(s):  
Strain Gradient ◽  
Scale Effects ◽  
Buckling Load ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Geometrical Parameters ◽  
Gradient Theory ◽  
Vast Number ◽  
Non Local ◽  
The Galerkin Method

AbstractIn recent years, nanostructures have been used in a vast number of applications, making the study of the mechanical behaviour of such structures important. In this paper, two different constitutive equations including first-order strain gradient and simplified differential non-local are employed to model the buckling behaviour of skew nanoplates. The Galerkin method is used for solving the equations in order to obtain buckling load. Using this method, the influence of different parameters consisting of non-classical properties, boundary conditions, and geometrical parameters such as length and angle on the buckling load, are studied. The results showed that small-scale effects are very important in skew graphene sheets and their inclusion results in smaller buckling loads.

Nonlinear Pull-In Instability of Strain Gradient Microplates Made of Functionally Graded Materials

2019 ◽  
Vol 19 (02) ◽  
pp. 1950007 ◽  
Author(s):  
R. Gholami ◽  
R. Ansari ◽  
H. Rouhi
Keyword(s):  
Functionally Graded Materials ◽  
Strain Gradient ◽  
Scale Effects ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Graded Materials ◽  
First Order ◽  
Size Dependent

In this paper, the size-dependent nonlinear pull-in behavior of rectangular microplates made from functionally graded materials (FGMs) subjected to electrostatic actuation is numerically studied using a novel approach. The small scale effects are taken into account according to Mindlin’s first-order strain gradient theory (SGT). The plate model is formulated based on the first-order shear deformation theory (FSDT) using the virtual work principle. The size-dependent relations are derived in general form, which can be reduced to those based on different elasticity theories, including the modified strain gradient, modified couple stress and classical theories (MSGT, MCST and CT). The solution of the problem is arrived at by employing an efficient matrix-based method called the variational differential quadrature (VDQ). First, the quadratic form of the energy functional including the size effects is obtained. Then, it is discretized by the VDQ method using a set of matrix differential and integral operators. Finally, the achieved discretized nonlinear equations are solved by the pseudo arc-length continuation method. In the numerical results, the effects of material length scale parameters, side length-to-thickness ratio and FGM’s material gradient index on the nonlinear pull-in instability of microplates with different boundary conditions are investigated. A comparison is also made between the predictions by the MSGT, MCST and CT.

Nonlinear Vibration Analysis of a Fractional Viscoelastic Euler-Bernoulli Microbeam

2018 ◽  
Author(s):  
Firooz Bakhtiari-Nejad ◽  
Ehsan Loghman ◽  
Mostafa Pirasteh
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Multiple Scales ◽  
Scale Effects ◽  
Viscoelastic Model ◽  
Harmonic Excitation ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Harmonic Resonance

Nonlinear vibration of a simply-supported Euler-Bernoulli microbeam with fractional Kelvin-Voigt viscoelastic model subjected to harmonic excitation is investigated in this paper. For small scale effects the modified strain gradient theory is used. For take into account geometric nonlinearities the Von karman theory is applied. Beam equations are derived from Hamilton principle and the Galerkin method is used to convert fractional partial differential equations into fractional ordinary differential equations. Problem is solved by using the method of multiple scales and amplitude-frequency equations are obtained for primary, super-harmonic and sub-harmonic resonance. Effects of force amplitude, fractional parameters and nonlinearity on the frequency responses for primary, super-harmonic and sub-harmonic resonance are investigated. Finally results are compared with ordinary Kelvin-Voigt viscoelastic model.

Buckling and frequency analysis of the nonlocal strain–stress gradient shell reinforced with graphene nanoplatelets

2019 ◽  
Vol 25 (19-20) ◽  
pp. 2627-2640 ◽  
Author(s):  
Masoud Mohammadgholiha ◽  
Ali Shokrgozar ◽  
Mostafa Habibi ◽  
Hamed Safarpour
Keyword(s):  
Boundary Conditions ◽  
Differential Quadrature Method ◽  
Nonlocal Parameter ◽  
Stress Gradient ◽  
Graphene Nanoplatelets ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Various Boundary Conditions ◽  
Pattern Length

In this study, buckling and vibrational characteristics of a nanoshell reinforced with graphene nanoplatelets under uniform axial load are investigated. The material properties of the piece-wise graphene-reinforced composites (GPLRCs) are assumed to be graded in the thickness direction of a nanoshell and are estimated using a nanomechanical model. The effects of the small scale are analyzed based on nonlocal stress–strain gradient theory (NSGT). The governing equations and boundary conditions (BCs) are developed using Hamilton’s principle and are solved with assistance of the generalized differential quadrature method. The novelty of the current study is the consideration of GPLRC and size effect as well as satisfying various boundary conditions implemented on the proposed model using NSGT. The results show that, nonlocal parameter, graphene platelet (GPL) distribution pattern, length scale parameter, number of layers, and GPL weight function have significant influence on the buckling and natural frequency of the GPLRC nanoshell. Another significant result is that nonlocal parameter does not have any effect on the buckling load for each BC. The results of the current study are useful for design of the nanoactuators and nanosensors.

scholarly journals Free Vibration of Functionally Graded Carbon Nanotube-reinforced Doubly-curved Shells

2020 ◽  
Vol 01 ◽  
Author(s):  
Maziar Janghorban ◽  
Behrouz Karami
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Strain Gradient ◽  
Shear Deformation Theory ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Size Dependency ◽  
Wide Range ◽  
Doubly Curved

Background:: Carbon nanotubes (CNTs) reinforced structures are the main elements of structural equipment. Hence a wide range of investigations has been performed on the response of these structures. A lot of studies covered the static and dynamic phenomenon of CNTs reinforced beams, plates and shells. However, there is no study on the free vibration analysis of a doubly-curved nano-size shell made of CNTs reinforced composite materials. Methods:: This work utilized a general third-order shear deformation theory to model the nanoshell where the general strain gradient theory is used in order to capture both nonlocality and strain gradient size-dependency. The Navier solution solving procedure is adopted to solve the partial differential equations (PDEs) and get the natural frequency of the system which is obtained through the Hamilton principle. Results:: The current study shows the importance of small-scale coefficients. The natural frequency increases with rising the strain gradient-size dependency which is because of stiffness enhancement, while the natural frequency decreases by increasing the nonlocality. In addition, the numerical examples covered the CNTs distribution patterns. Conclusion:: This work also studied the importance of shell panel’s shape. It has been observed that spherical shell panel has a higher frequency compared to the hyperbolic one. Furthermore, the frequency of the system increases with growing length-to-thickness ration.

Size-Dependent Strain Gradient-Based Thermoelastic Damping in Micro-Beams Utilizing a Generalized Thermoelasticity Theory

2019 ◽  
Vol 11 (01) ◽  
pp. 1950007 ◽  
Author(s):  
Vahid Borjalilou ◽  
Mohsen Asghari
Keyword(s):  
Heat Conduction ◽  
Strain Gradient ◽  
Scale Effects ◽  
Generalized Thermoelasticity ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Phase Lag ◽  
Thermoelastic Damping ◽  
Coupled Equations

The small-scale effects on the thermoelastic damping (TED) in Euler–Bernoulli micro-beams is investigated in this study. To this purpose, by utilizing the strain gradient theory (SGT) and the dual-phase-lag (DPL) heat conduction model, the coupled equations of motion and heat conduction are derived. By solving these equations simultaneously and using the Galerkin method, the real and imaginary parts of the frequency and the amount of TED in thin micro-beams are obtained. The results predicted by SGT are compared with those given by the modified couple stress theory (MCST) and the classical continuum theory. In addition, TED is calculated on the basis of energy dissipation approach which shows that the difference between the obtained results and those evaluated based on the frequency approach is negligible. Some numerical results are also presented in order to study the effects of different parameters of the micro-beams as well as the type of the boundary conditions on TED and the critical thickness; these parameters include the micro-beam height, its aspect ratio and type of the material.

Flexural Vibration Characteristics of Micro-Rotors Based on the Strain Gradient Theory

2015 ◽  
Vol 07 (05) ◽  
pp. 1550075 ◽  
Author(s):  
Mohsen Asghari ◽  
Mehdi Hashemi
Keyword(s):  
Strain Gradient ◽  
Natural Frequencies ◽  
Scale Effects ◽  
Equations Of Motion ◽  
Complex Form ◽  
Flexural Vibration ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Rotating Shaft

In this paper, the coupled three-dimensional flexural vibration of micro-rotors is investigated by taking into account the small-scale effects utilizing the strain gradient theory, which is a powerful nonclassical continuum theory in capturing small-scale effects. A micro-rotor consists mainly of a flexible micro-rotating shaft and a disk. With the aid of Hamilton's principle, governing equations of motion are derived and then transformed to the complex form. By implementing the Galerkin's method, a coupled ordinary differential equation is attained for the system. Expressions for the first two natural frequencies of the spinning micro-rotors are obtained with truncated two-term equation. Parametric studies on the results for different responses illustrate that the values of higher-order material constants may have significant effects on the natural frequencies of the system.

scholarly journals Comparison between using generalized differential quadrature method and analytical solution in analyzing vibration behavior of nonuniform nanobeam systems

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Hossein Bakhshi Khaniki1 ◽  
Shahrokh Hosseini Hashemi2 ◽  
Hossein Bakhshi Khaniki2
Keyword(s):  
Scale Effects ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Elastic Theory ◽  
Small Scale ◽  
Quadrature Method ◽  
Generalized Differential Quadrature Method ◽  
Sampling Points ◽  
Generalized Differential ◽  
Nonlocal Elastic Theory

In this article, generalized differential quadrature method (GDQM) is used to study the free vibrational behavior of variable cross section nano beams. Eringen's nonlocal elastic theory is taken into account to model the small scale effects and nonuniformity is assumed by exponentially varying the width of nano beam. Governing equation of motion is solved using generalized differential quadrature method with different numbers of sampling points. Effects of increasing the sampling points in reaching more accurate results for first three frequency parameters are presented and it is shown that after a specific number of sampling points, results merge to a certain accurate number. It is concluded that generalized differential quadrature method is able to reach the correct answers comparing to analytical results. Moreover, due to the stiffness softening behavior of small-scale structures, necessity of using Eringen's nonlocal elastic theory to model the small scale effects due to the frequency variation is observed.

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