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.

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.

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.

Stress Analysis of a Functionally Graded Micro/ Nanorotating Disk with Variable Thickness Based on the Strain Gradient Theory

2016 ◽  
Vol 08 (02) ◽  
pp. 1650020 ◽  
Author(s):  
M. Baghani ◽  
N. Heydarzadeh ◽  
M. M. Roozbahani
Keyword(s):  
Variable Thickness ◽  
Strain Gradient ◽  
Mechanical Response ◽  
Rotating Disk ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Graded Materials ◽  
Remarkable Effect

In this paper, mechanical response of a micro/nanorotating disk made of functionally graded materials (FGMs) with variable thickness is investigated. Through utilizing variational method and considering the strain gradient theory, the governing equations and the boundary conditions are derived. In order to verify the developed formulation, in special limiting cases, the results are compared with those available in the literature. These comparisons show an excellent correspondence. Employing numerical techniques, some numerical results are presented to investigate the effect of variations of properties and thickness on the response of the small scale rotating disk. It is found that the non-homogeneity constants have a remarkable effect on the stress distribution in the FG rotating disk. Furthermore, the amount of stress could be reduced in the rotating disk through fabricating it with variable thickness.

Exact solution for bending analysis of functionally graded micro-plates based on strain gradient theory

2018 ◽  
Vol 25 (3) ◽  
pp. 439-451
Author(s):  
Meisam Mohammadi ◽  
Afshin Iranmanesh ◽  
Seyed Sadegh Naseralavi ◽  
Hamed Farahmand
Keyword(s):  
Boundary Conditions ◽  
Strain Gradient ◽  
Material Properties ◽  
Plate Theory ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Governing Equations ◽  
Micro Plates ◽  
Micro Structures

Abstract In the present article, static analysis of thin functionally graded micro-plates, based on Kirchhoff plate theory, is investigated. Utilizing the strain gradient theory and principle of minimum total potential energy, governing equations of rectangular micro-plates, subjected to distributed load, are explored. In accordance with functionally graded distribution of material properties through the thickness, higher-order governing equations are coupled in terms of displacement fields. Introducing a novel methodology, governing equations are decoupled, with special privilege of solving analytically. These new equations are solved for micro-plates with Levy boundary conditions. It is shown that neutral plane in functionally graded micro-plate is moved from midplane to a new coordinate in thickness direction. It is shown that considering micro-structures effects affects the governing equations and boundary conditions. Finally, the effects of material properties, micro-structures, boundary conditions and dimensions are expounded on the static response of micro-plate. Results show that increasing the length scale parameter and FGM index increases the rigidity of micro-plate. In addition, it is concluded that using classical theories for study of micro-structures leads to inaccurate results.

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.

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