Sharif Digital Repository

In this paper, the classical and nonlocal elasticity are applied to investigate the deflection and instability of electrostatically actuated carbon nanotubes. The results are presented for different geometries and boundary conditions. They reveal that increasing radius and gap and decreasing length confine to increasing pull-in voltages of the carbon nanotubes. The results prove that application of the nonlocal elasticity theorem leads to stiffer structures with higher pull-in voltages. Thus, in order to obtain more accurate results about the mechanical and electromechanical behaviors of the carbon nanotubes, one should apply the nonclassical elasticity theories such as that applied in this... 

The paper investigates the effects of application of nonlocal elasticity theory on electromechanical behaviors of single-walled carbon nanotubes under electrostatic actuation. The influences of different dimensions and boundary conditions on the vibration and dynamic instability of the carbon nanotubes are studied, in detail, using this theory. The results reveal that application of the non-local elasticity theory leads to the higher pull-in voltages for the nonlocal model applied for carbon nanotubes. Thus, in order to have more accurate results, one should apply nonclassical theorems such as the nonlocal elasticity theory to scrutinize the mechanical and electromechanical behaviors of the... 

This Letter aims at the investigation of free-vibration properties of nanocones based on a nonlocal continuum shell model. A novel approach is used for derivation of the governing equations of motion and the Galerkin technique is used to obtain the natural frequencies of vibrations. The effects of small-scale and geometrical parameters of the nanocone on the natural frequencies are studied and some conclusions are drawn  

In this paper, a nonlocal elasticity formulation is presented for analyzing the instability of nano-peapods by modeling the nanotube as a shell. Using the nonlocal elasticity theory, the small scale characteristics of Carbon Nano-Peapods (CNPs) are taken into account. While the classical elastic shell model overestimates the critical pressure for the onset of structural instability of carbon nanotubes, the obtained results show that the nonlocal elastic shell model for nano-peapods can potentially provide better predictions. According to the results, it is concluded that the presence of C 60 inside (10,10) Carbon Nanotubes (CNTs) significantly increases the stability resistance of the single... 

A nonlocal continuum shell model is developed to study the stability of nanocones under combined loading: external pressure and compression force. The nonlinear governing equations of motion of nanocone are obtained using Hamiltons principle and the external loads are considered as prestress. Based on Eringens nonlocal elasticity theory the small-scale effect is accounted in the governing equations of motion. To obtain the critical loads, the equations are solved using Galerkin technique and the effect of small-scale parameter and geometry on the stability of nanocone is studied  

Stress distribution in Carbon Nanotube (CNT) reinforced composites is studied using nonlocal theory of elasticity. Two nearby CNTs are modeled as two circular inclusions embedded in an infinite elastic medium, and classical stresses are obtained using the complex stress potential method. Nonlocal stresses are calculated using nonlocal integral elasticity equation. Effects of the distance between CNTs as well as effects of the nonlocal parameters on the stress distribution and stress concentration are studied. For unit normal stress at infinity, stress at the interface of the CNT and matrix increases from 0.1 for classical analysis to 0.85 for nonlocal analysis. Furthermore, when two CNTs... 

In this paper we shall argue that conformal transformations give some new aspects to a metric and changes the physics that arises from the classical metric. It is equivalent to adding a new potential to relativistic Hamilton-Jacobi equation. We start by using conformal transformations on a metric and obtain modified geodesics. Then, we try to show that extra terms in the modified geodesics are indications of a background force. We obtain this potential by using variational method. Then, we see that this background potential is the same as the Bohmian non-local quantum potential. This approach gives a method stronger than Bohm's original method in deriving Bohmian quantum potential. We do not... 

In this paper, a computational counterpart of the experimental investigation is presented based on a nonlocal computational homogenization technique for extracting damage model parameters in quasi-brittle materials with softening behavior. The technique is illustrated by introducing the macroscopic nonlocal strain to eliminate the mesh sensitivity in the macroscale level as well as the size dependence of the representative volume element (RVE) in the first-order continuous homogenization. The macroscopic nonlocal strains are computed at each direction, and both the local and nonlocal strains are transferred to the microscale level. Two RVEs with similar geometries and material properties are... 

In this paper, we consider the problem of simulating one copy of a zero-capacity two-way channel from arbitrary many copies of another two-way channel. The motivation for this problem comes from foundation of quantum physics where zero-capacity two-way channels (a.k.a. no-signaling boxes) serve as the abstract objects for studying non-locality. We provide necessary conditions for the possibility of channel simulation using two measures of correlation, namely maximal correlation and hypercontractivity ribbon. It is shown that when these measures are defined appropriately for two-way channels, they are monotonically decreasing under local operations. Our result allows us to establish a... 

A single-walled nanotube structure embedded in an elastic matrix is simulated by the nonlocal EulerBernoulli, Timoshenko, and higher order beams. The beams are assumed to be elastically supported and attached to continuous lateral and rotational springs to take into account the effects of the surrounding matrix. The discrete equations of motion associated with free transverse vibration of each model are established in the context of the nonlocal continuum mechanics of Eringen using Hamilton's principle and an efficient meshless method. The effects of slenderness ratio of the nanotube, small scale effect parameter, initial axial force and the stiffness of the surrounding matrix on the natural... 

The nanostructures under rotation have high promising future to be used in nanomachines, nano-motors and nano-turbines. They are also one of the topics of interests and it is new in designing of rotating nano-systems. In this paper, the scaledependent vibration analysis of a nanoplate with consideration of the axial force due to the rotation has been investigated. The governing equation and boundary conditions are derived using the Hamilton's principle based on nonlocal elasticity theory. The boundary conditions of the nanoplate are considered as free-free in y direction and two clamped-free (cantilever plate) and clamped-simply (propped cantilever) in x direction. The equations have been... 

In this study, critical temperature and frequency characteristics of a doubly curved panel are reinforced by graphene nanoplatelets (GPLs) with the aid of a two-dimensional generalized differential quadrature method (2D-GDQM) are investigated. The size effects are included using nonlocal strain gradient theory (NSGT) that has two length scale parameters, and the panel is modeled as a panel using high order shear deformation theory (HSDT). The mechanical properties of GPLs are calculated based on the rule of mixtures and the modified Halpin-Tsai model. The novelty of the current study is in considering the effects of the thermal environment, various boundary conditions, and size effects on... 

The effect of elastic foundation on the free vibration characteristics of embedded nanocones is investigated in this paper. The nanocone is modeled as a thin shell and the nonlocal elasticity theory is used to derive the governing equations of motion. Also the elastic medium is simulated using Winkler and Pasternak foundation models. Based on the modal analysis technique and applying the Galerkin method the governing equations are solved to obtain the natural frequencies. The drawn results emphasis the effects of geometry and small-scale parameter on the natural frequencies of nanocone. Also the effect of elastic foundation modulus on the resonance frequencies of the nanocones are studied... 

In this paper, utilizing the non-local theory, the resonant frequency and sensitivity of an AFM microcantilever are investigated. To that end, the governing equation of motion and corresponding boundary conditions are obtained using the variational approach. Afterwards, the resonant frequency and sensitivity of the AFM microcantilever are derived analytically and depicted in some figures versus the contact stiffness of the sampling surface. The results of the current model are compared to those of the classical theory. The comparison shows that the difference between the results of the non-local theory and those of the classical theory is significant when the non-local parameter is high but... 

The free vibration analysis of rotating axially functionally graded nanobeams under an in-plane nonlinear thermal loading is provided for the first time in this paper. The formulations are based on Timoshenko beam theory through Hamilton’s principle. The small-scale effect has been considered using the nonlocal Eringen’s elasticity theory. Then, the governing equations are solved by generalized differential quadrature method. It is supposed that the thermal distribution is considered as nonlinear, material properties are temperature dependent, and the power-law form is the basis of the variation of the material properties through the axial of beam. Free vibration frequencies obtained are... 

Based on nonlocal strain gradient theory (NSGT), transient behavior of a porous functionally graded (FG) nanoplate due to various impulse loads has been studied. The porous nanoplate has evenly and unevenly distributed pores inside its material structure. Impulse point loads are considered to be rectangular, triangular and sinusoidal types. These impulse loads lead to transient vibration of the nanoplate which is not studied before. NSGT introduces a nonlocal coefficient together with a strain gradient coefficient to characterize small size influences due to non-uniform stress and strain fields. Galerkin's approach has been performed to solve the governing equations and also inverse Laplace...