scholarly journals A Note on Torsion of Nonlocal Composite Nanobeams

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Luciano Feo ◽  
Rosa Penna
Keyword(s):  
Order Differential Equation ◽  
Scale Effects ◽  
Elastic Equilibrium ◽  
Functionally Graded ◽  
Small Scale ◽  
Cross Sectional ◽  
Graded Materials ◽  
First Order ◽  
Sectional Plane ◽  
Mixed Framework

The ERINGENelastic constitutive relation is used in this paper in order to assess small-scale effects in nanobeams. Structural behavior is studied for functionally graded materials in the cross-sectional plane and torsional loading conditions. The governing boundary value problem has been formulated in a mixed framework. Torsional rotations and equilibrated moments are evaluated by solving a first-order differential equation of elastic equilibrium with boundary conditions of kinematic-type. Benchmarks examples are briefly discussed, enlightening thus effectiveness of the proposed methodology.

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.

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.

Bending and free vibration analyses of functionally graded material nanoplates via a novel nonlocal single variable shear deformation plate theory

2020 ◽  
pp. 095440622096452
Author(s):  
Le Kha Hoa ◽  
Pham Van Vinh ◽  
Nguyen Dinh Duc ◽  
Nguyen Thoi Trung ◽  
Le Truong Son ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Functionally Graded Material ◽  
Numerical Solutions ◽  
Scale Effects ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Small Scale ◽  
Parameter Study ◽  
Graded Material

A novel nonlocal shear deformation theory is established to investigate functionally graded nanoplates. The significant benefit of this theory is that it consists of only one unknown variable in its displacement formula and governing differential equation, but it can take into account both the quadratic distribution of the shear strains and stresses through the plate thickness as well as the small-scale effects on nanostructures. The numerical solutions of simply supported rectangular functionally graded material nanoplates are carried out by applying the Navier procedure. To indicate the accuracy and convergence of this theory, the present solutions have been compared with other published results. Furthermore, a deep parameter study is also carried out to exhibit the influence of some parameters on the response of the functionally graded material nanoplates.

scholarly journals On Bending of Bernoulli-Euler Nanobeams for Nonlocal Composite Materials

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Luciano Feo ◽  
Rosa Penna
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Scale Parameter ◽  
Elastic Equilibrium ◽  
Functionally Graded ◽  
Constitutive Law ◽  
Bending Moments ◽  
Innovative Methodology ◽  
Governing Differential Equation ◽  
Nonlocality Effect

Evaluation of size effects in functionally graded elastic nanobeams is carried out by making recourse to the nonlocal continuum mechanics. The Bernoulli-Euler kinematic assumption and the Eringen nonlocal constitutive law are assumed in the formulation of the elastic equilibrium problem. An innovative methodology, characterized by a lowering in the order of governing differential equation, is adopted in the present manuscript in order to solve the boundary value problem of a nanobeam under flexure. Unlike standard treatments, a second-order differential equation of nonlocal equilibrium elastic is integrated in terms of transverse displacements and equilibrated bending moments. Benchmark examples are developed, thus providing the nonlocality effect in nanocantilever and clampled-simply supported nanobeams for selected values of the Eringen scale parameter.

Dynamic Response of Cantilever FGM Cylindrical Shell

2011 ◽  
Vol 130-134 ◽  
pp. 3986-3993 ◽  
Author(s):  
Yu Xin Hao ◽  
Wei Zhang ◽  
L. Yang ◽  
J.H. Wang
Keyword(s):  
Cylindrical Shell ◽  
Volume Fraction ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Graded Materials ◽  
First Order ◽  
Two Degree Of Freedom

An analysis on the nonlinear dynamics of a cantilever functionally graded materials (FGM) cylindrical shell subjected to the transversal excitation is presented in thermal environment.Material properties are assumed to be temperature-dependent. Based on the Reddy’s first-order shell theory,the nonlinear governing equations of motion for the FGM cylindrical shell are derived using the Hamilton’s principle. The Galerkin’s method is utilized to discretize the governing partial equations to a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms under combined external excitations. It is our desirable to choose a suitable mode function to satisfy the first two modes of transverse nonlinear oscillations and the boundary conditions for the cantilever FGM cylindrical shell. Numerical method is used to find that in the case of non-internal resonance the transverse amplitude are decreased by increasing the volume fraction index N.

Thermo-Micromechanical Vibration Behaviors of FGM Structures with Neutral Surface

2017 ◽  
Vol 864 ◽  
pp. 162-166
Author(s):  
Tae Kyung Lim ◽  
Ji Hwan Kim
Keyword(s):  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Elastic Vibration ◽  
Functionally Graded ◽  
Reference Plane ◽  
Neutral Surface ◽  
Temperature Dependent ◽  
Graded Materials ◽  
First Order ◽  
Mechanical Models

This work presents the micro-mechanical models in thermal environment for the vibration behavior of Functionally Graded Materials (FGMs) plate using First-order Shear Deformation Theory (FSDT). In the formulation, the heat transfer effects and the temperature-dependent material properties are considered. Relative estimation of micromechanical behaviors of Mori-Tanaka Method (MTM) is used. And, neutral surface concept is adopted as the reference plane due to the asymmetry in the thickness direction of the model. In the numerical analysis, Finite Element Method is applied for various volume fractions and temperature rising conditions. Also Power-law and Sigmoid FGMs are discussed in thermo-elastic vibration characteristics.

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.

scholarly journals Finite Element Analysis of the Deformation of Functionally Graded Plates under Thermomechanical Loads

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
A. E. Alshorbagy ◽  
S. S. Alieldin ◽  
M. Shaat ◽  
F. F. Mahmoud
Keyword(s):  
Volume Fraction ◽  
Thermomechanical Behavior ◽  
Functionally Graded ◽  
Neutral Plane ◽  
Functionally Graded Plates ◽  
Element Analysis ◽  
Graded Materials ◽  
First Order ◽  
Fg Plates ◽  
Continuous Power

The first-order shear deformation plate model, accounting for the exact neutral plane position, is exploited to investigate the uncoupled thermomechanical behavior of functionally graded (FG) plates. Functionally graded materials are mainly constructed to operate in high temperature environments. Also, FG plates are used in many applications (such as mechanical, electrical, and magnetic), where an amount of heat may be generated into the FG plate whenever other forms of energy (electrical, magnetic, etc.) are converted into thermal energy. Several simulations are performed to study the behavior of FG plates, subjected to thermomechanical loadings, and focus the attention on the effect of the heat source intensity. Most of the previous studies have considered the midplane neutral one, while the actual position of neutral plane for functionally graded plates is shifted and should be firstly determined. A comparative study is performed to illustrate the effect of considering the neutral plane position. The volume fraction of the two constituent materials of the FG plate is varied smoothly and continuously, as a continuous power function of the material position, along the thickness of the plate.

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