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In this paper, the Chebyshev collocation numerical method is developed for solving generalized thermoelasticity problems of the isotropic homogeneous two dimensional media. The coupled thermoelasti...

In this paper, transient coupled heat and moisture transfer in the cylinders and cylindrical panels of the porous medium are analyzed with three-dimensional finite element methods. Both Dofour and Soret effects are considered in the formulation, and the FEM-based weak forms of the equations are derived using Galerkin method. In the full cylinder cases, both symmetrical and unsymmetrical boundary conditions for heat and moisture are applied to cover three-dimensional and axisymmetric (two dimensional) analysis cases. The obtained systems of time-dependent differential equations are solved by Runge–Kutta method. The main objective of the present study is the analysis of fully coupled diffusion of heat and moisture in cylindrical coordinates using three-dimensional finite element methods. Also, this study addressed the ability of Runge–Kutta method to solve the coupled sets of differential equations. The results were compared with some analytical solutions in the literature, and a very good agreement was observed. The present formulation can be used for transient analysis of any cylindrical geometry with arbitrary geometrical dimensions and under desired boundary conditions.

In this article, the Chebyshev collocation numerical method is developed for solving generalized thermoelasticity problems of the isotropic layer. The coupled thermoelastic equations are derived ba...

In this paper, the effect of electric field on axial buckling of boron nitride nanotubes is investigated. For this purpose, molecular dynamics simulation and continuum mechanics are used for the first time simultaneously. In molecular dynamics simulation, the potential between boron nitride atoms is considered as Tersoff and Timoshenko beam theory is used in continuum mechanics. In this paper, buckling of zigzag and armchair boron nitride nanotubes are investigated. Here, the effects of the electric field and the length of the boron nitride nanotube on the critical load are investigated and it is shown that the effect of the electric field is different with respect to the arrangement of atoms in the boron nitride nanotubes. In fact, the electric field creates axial and torsional loads on the zigzag and armchair nanotube, respectively. Axial buckling of the zigzag nanotube is dependent on the electric field, whereas in the armchair nanotubes, the electric field changes have no effect on the axial buckling. To better understand the impact of the electric field on axial buckling, these results are compared with the continuum mechanics.

In this article, a highly efficient quasi-three-dimensional theory has been used to study the nonlinear hygro-thermo-mechanical bending analysis of a very thick functionally graded material (FGM) r...

In this study, size-dependent nonlinear forced vibration of viscoelastic/flexoelectric nanobeams has been investigated. By calculating enthalpy and kinetic energy and using Hamilton’s principle, the coupled governing equations of viscoelastic/flexoelectric nanobeams are derived along with dependent electrical and mechanical boundary conditions. Furthermore, to take the effects of the small scale into account, the nonclassical theory of continuous medium has been used and the Euler–Bernoulli beam model has been adopted to model the nanobeams. Finally, the governing equations are solved using numerical methods for distributed loaded and clamped–clamped boundary conditions. By comparing the results, it is determined that the parameters of the size effect and the viscoelastic medium effect can increase the vibrational frequency of the nanobeams. Also, the results show that the frequency of nanobeams outside of the viscoelastic medium strongly depends on the size-dependent parameters, and the increase in the length and thickness of the nanobeam decreases the frequency. The results also show that with the increasing flexoelectric effect, the amplitude of the nonlinear oscillation increases.

In the present study, a continuous-based thermo-electromechanic model has been developed by the Kirchhoff plate’s theory and the modified flexoelectric theory in order to study the size-dependent nonlinear free vibration of functionally graded flexoelectric nano-plate under the magnetic field. Using the Hamilton’s principle and variation method, the nonlinear governing differential equations of the nano-plate and their associated boundary conditions have been extracted and the governing equations solved by using Galerkin’s and perturbation methods. The electromechanical coupling (electromechanical stress) in the internal energy function causes nonlinearity in the governing equations. The applied magnetic field is a type of external static field along with the nano-plate thickness. The natural frequencies and related mode shapes have been determined in two modes of direct and inverse flexoelectric effects. Also, the effects of such factors as length scale parameters, geometric parameters, thermal, magnetic and electrical loadings were investigated. In the presence of flexoelectric effect, the results showed that the dependence of electromechanical behavior of the structure on size is found to be significant in nanoscales. Regarding the application of this type of nano-plate in the oscillators and considering the flexoelectric effect, the applied potential difference can play an important role in adjusting and controlling the frequency.

In this paper, the effect of surface roughness on the pull-in behavior of beam-type nano-actuator in the presence of intermolecular Van der Waals force has been investigated. In order to model the surface roughness, the roughness has been modeled as a step on the fixed electrode. Based on the modified couple stress theory and by using Hamilton’s principle, the governing equation and boundary conditions have been derived for the Euler–Bernoulli beam model. The differential quadrature method has been used to solve the nonlinear governing equations of the system. The results showed that the presence of roughness on the fixed electrode leads to an increase in the displacement of the beam and a reduction in the pull-in voltage, especially when the roughness is at the end of the beam and has considerable height. In this case, the freestanding behavior of the nano-actuator and the effect of roughness on the critical intermolecular force in the absence of electrostatic force are also evaluated. The results revealed a decrease in the critical intermolecular force due to the presence of roughness. However, increasing the material length scale parameters leads to an increase in the pull-in voltage and the freestanding values. Also, the size effect parameter decreases the displacement at the end of the beam.

This paper analyzes the dynamic stability of an isotropic viscoelastic Euler–Bernoulli nano-beam using piezoelectric materials. For this purpose, the size-dependent theory was used in the framework of the modified couple stress theory (MCST) for piezoelectric materials. In order to capture the geometrical nonlinearity, the von Karman strain displacement relation was applied. Hamilton’s principle was also employed to obtain the governing equations. Furthermore, the Galerkin method was used in order to convert the governing partial differential equations (PDEs) to a nonlinear second-order ordinary differential one. Dynamic stability analysis was performed and the effects of such parameters as viscoelastic coefficients, size effect, and piezoelectric coefficient were investigated. The results showed that in this system, saddle points, central points, Hopf bifurcation points, and fork bifurcation points could be created, and the phase portraits connecting these equilibrium points exhibit periodic orbits, heteroclinic orbits, and homoclinic orbits.

In this paper, axial buckling of boron nitride nanotubes (BNNTs) has been investigated. In order to achieve this purpose, the molecular dynamics was adopted and the potential between the at...

In this investigation, a transient nonlinear dynamic analysis of nanobeams reinforced with carbon nanotubes, which is located on a nonlinear viscoelastic foundation under the impulse loading, is investigated. The boundary conditions of the nanobeam are considered as clamped-clamped, and the carbon nanotube is distributed in different distribution along the thickness of nanobeam. First, using the Hamiltonian method and taking advantage of the couple stress theory and considering the Von Karman relationship between strain and displacement, the differential equation governing for Euler–Bernoulli nanobeam is obtained. Then, by using the semi-exact method and the Galerkin's method, the displacement derivatives are separated from the time derivatives and the equation derived is solved using Runge–Kutta's numerical method. In order to confirm the equation and its solution, a comparative study is performed that shows an appropriate fitting between the results. Finally, the influence of parameters such as nonlinear coefficient of foundation, applied force, size effect, and type of nanotube distribution on the nonlinear frequency to linear frequency ratio and transient nanobeam dynamic response is investigated. A study is also conducted on the effect of foundation damping coefficient and the inclusion of nonlinear effects on the transient dynamic response when the nanobeam is under impulse load and resonance conditions. The results show that the nonlinear vibrational frequency of the nanobeam with the FG-X carbon nanotube distribution is the highest, and the FG-O carbon nanotubes distribution is the least.

In this paper, triangular prismatic cells for background integration on mesh-free methods are introduced and the Gauss integration scheme is developed in these cells. The cells are used in the mesh-free Galerkin method for free vibration, static and dynamic analysis of general polygonal plates of various thicknesses. The moving least square shape functions are used to construct the approximation of field variables, and the Hamilton principle is used to drive the weak form equations of motion. For the dynamic case, the resulted set of differential equations are solved by the Wilson method. The main objective of this work is developing of a mesh-free method for analysis of triangle and polygonal geometries and more important is to use the triangular prismatic cells and corresponding generalized Gaussian quadrature rules for integration in mesh-free methods. The cells can be used in a compound with cubic cells for discretization of any complicate three-dimensional geometries. To show this capability, free vibration analysis of a general pentagon plate is also performed. For all cases, the results show the flexibility and accuracy of mesh-free methods for irregular and complicate sharp corner geometries.

In this study, the nonlinear dynamical response of a graded carbon nanotube-reinforced beam with graded shape memory wire has been investigated regarding the instantaneous variations of martensite ...

The present paper studies the thermo-electro-magnetic mechanical behavior of a flexoelectric nano-plate using a modified flexoelectric theory and application of classical Kirchhoff plate theory. Size and flexoelectric effects are considered. Using the variation method and the principle of minimum potential energy in the coupling form, for the first time, the nonlinear governing differential equations of the nano-plate and the relevant boundary conditions are obtained. The nano-plate is subjected to mechanical, electrical, magnetic and thermal loadings and is simply supported on all edges. Moreover, in the present study, analytical solutions are presented to investigate the effects of length scale parameters, geometric parameters, mechanical loading, and temperature rise of the nano-plate lower surface, the external electric potential, and the external static magnetic flux density on the magneto-thermo-electro-elastic behavior of the nano-plate. In order to verify the presented formulations, the results are compared to analytical results found in the literature. Due to high stain gradients in nano-scales, the results indicate that the flexoelectricity has a larger influence in plates with smaller thicknesses. The results also show that, in the presence of flexoelectricity and static magnetic field, the rigidity of the nano-plate increases. Also, the deflection and the generated electric potential along nano-plate thickness decrease.

In this paper, two-node size-dependent axisymmetric shell element formulation is developed by using thin conical shell model in the place of the beam model, which is used in previous research and using the modified couple stress theory in the place of the classical continuum theory. Since classical continuum theory is unable to correctly compute stiffness and account for size effects in micro/nanostructures, higher order continuum theories such as modified couple stress theory have become quite popular. The mass stiffness matrix and geometric stiffness matrix for axisymmetric shell element are developed in this paper, and by means of size-dependent finite element formulation it is extended to more precisely account for nanotube buckling. The results have indicated using the two-node axisymmetric shell element, where the rigidity of the nano-shell is greater than that in the classical, and the critical axial buckling loads obtained from couple stress theory are greater than that of classical, which is due to the presence of one size parameter in couple stress theory. The findings also indicate that the developed size-dependent axisymmetric shell element is able to analyze the buckling of cylindrical and conical shells and also circular plate, which is reliable for simulating micro/nanostructures and can be used for the analysis of size effect and has desirable convergence characteristic. Besides, in addition to reducing the number of elements required, using axisymmetric shell element also increases convergence speed and accuracy.

A new method has been presented for static analysis of macro- and nano sector plates with variable thickness. The thickness variations are assumed linearly, functionally, and also irregular...

This paper studies the free vibration of polymer nanocomposite reinforced by graphene sheet. In this work, the new size dependent formulation is presented for nanocomposites based on couple stress theory. For this purpose, the first shear deformation theory is applied. The effect of scale parameter is investigated based on anisotropic couple stress theory. Vibration equations of the composite lamina are extracted using Hamilton’s principle. Numerical results are provided for Poly methyl methacrylate/graphene composite.Mechanical properties of the composite are obtained from molecular dynamics simulation. Based on eigenvalue procedure, an analytical solution is obtained for the natural frequency of composite lamina. In the results section, the effect of dimensional and physical parameters are investigated on lamina natural frequency. It is observed that graphene defects caused to diminish the lamina frequency. Furthermore, it is revealed that the increase in graphene volume fraction leads to natural frequency be greater.

This study was conducted with the aim of investigating the Newtonian nanofluid flow in a catheterized tapered artery through using a completely consistent couple stress theory. In the process of carrying out this study, the slip condition at the arterial wall and the catheter, as well as, the permeability was taken into account. Further, the velocity, temperature, and concentration profiles were analytically modeled and the effect of the length scale on these profiles was well presented through the way it influences small-scale flows. The effect of the slip condition at the artery and catheter walls on the velocity was also investigated and revealed that any increase in the velocity leads to an increase in the slip velocity. Furthermore, the effect of other parameters such as the catheter diameter, shape, and height of the stenosis on these profiles was explored for all three artery geometries, i.e., diverging tapered artery, converging tapered artery, and non-tapered artery, respectively. The findings suggested that any increase in the catheter diameter and stenosis height can decrease the velocity and nanoparticle concentration profiles, while the temperature profile increases. It was also found that by increasing the stenosis shape parameter the velocity and concentration profiles increase and temperature decreases.

In this paper, size dependent axisymmetric shell element formulation is developed by using the modified couple stress theory in place of classical continuum theory. Since the study of nanoshells is conducted in nanodimensions, the mechanical properties of nanoshells are size dependent; therefore, taking into consideration the size effect, nonclassical continuum theories are used. In the present work the mass–stiffness matrix for axisymmetric shell element is developed, and by means of size-dependent finite element, the formulation is extended to more precisely account for nanotube vibration. It is shown that the classical axisymmetric shell element can also be defined by setting length scale parameter to zero in the equations. The results show that the rigidity of the nanoshell in the modified couple stress theory is greater than that in classical continuum theory, which leads to the increase in natural frequencies. The findings also indicate that the developed size dependent axisymmetric shell element is able to cover both cylindrical and conical shell elements and is reliable for simulating micro/nanoshells. Using size dependent axisymmetric shell element increases convergence speed and accuracy in addition to reducing the number of the required elements.

This research presents numerical and micromechanical investigations of the effects of carbon nanotube (CNT) weight fraction on nanocomposites fracture energy. For this reason, numerical models cons...

In this paper, the vibration and instability of double-walled carbon nanotube (DWCNT) conveying fluid were investigated by using the modified strain gradient theory. The Donnell's shell theory was used by taking into consideration the three size effects and simply-supported boundary conditions. The effect of van der Waals force between the two intended walls and the surroundings of the DWCNT was modelled as visco-Pasternak foundation. The governing equations of the problem and boundary conditions were derived from Hamilton’s principle. Also, Navier procedure was used to solve the vibration problem. To verify the results, a comparison was drawn between the results of this study and those of the references. According to the findings, the effects of fluid velocity, stiffness and damping of visco-Pasternak foundation, length of DWCNT and size effect are more considerable in the modified strain gradient theory than in the modified couple stress theory and classical theory. Keywords: Modified strain gradient theory, Donnell’s shell theory, DWCNT, size effect, shell vibration.

Wave propagation in viscoelastic single walled carbon nanotubes is investigated by accounting for the simultaneous effects of the nonlocal constant and the material length scale parameter. To this end, thin shell theory is used to model the viscoelastic single walled carbon nanotubes, and the nonlocal strain gradient theory is used to account for the effects of the nonlocal constant and the material length scale parameter. The Kelvin–Voigt model is used to model the viscoelastic property, and the governing equations are derived through Hamilton’s principle. The viscoelastic single walled carbon nanotube medium is modeled as visco-Pasternak. The results demonstrate that viscoelastic single walled carbon nanotube rigidity is higher in the strain gradient theory and lower in the nonlocal theory in comparison to that in the classical theory. Also, the size effects, nanotube radius, circumferential wavenumber, nanotube damping coefficient, and foundation damping coefficient exert considerable effects on viscoelastic single walled carbon nanotube phase velocity.

In this paper, the size-dependent free vibration of magneto-electro-elastic (MEE) nanobeams in thermal environment is investigated. Size effects are taken into account using the modified co...

In this study, wave propagation in functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical microshell is investigated by taking into consideration nonlocal constant and material length scale parameter. For this purpose, FG-CNTRC cylindrical microshell is modeled using shear deformable shell theory as well as nonlocal strain gradient theory. The classical governing equations are extracted using Hamilton’s principle. Carbon nanotubes are distributed in UD and FG-X shapes in FG-CNTRC cylindrical microshells. The results demonstrate that the rigidity of FG-CNTRC cylindrical microshell is higher in the strain gradient theory and lower in the nonlocal theory compared to that in the classical theory. In addition, the effect of manner of distribution of carbon nanotubes in the FG-CNTRC cylindrical microshell as well as the effect of volume fraction of the carbon nanotubes on the phase velocity of the FG-CNTRC cylindrical microshell is investigated. The results demonstrate that the effects of nonlocal constant and material length scale parameter, thickness, and wavenumber on the phase velocity of FG-CNTRC cylindrical microshell are considerable.

Functionally graded piezoelectric materials are of interest for a wide variety of nanotechnological applications. Buckling of functionally graded piezoelectric nanotubes, as ubiquitous event, recently attracted increasing interest. Also, in this article, the buckling response of bimorph functionally graded piezoelectric cylindrical nanoshells attended to lateral pressure is investigated on the basis of nonlocal strain gradient theory. The formulation developed on the basis of the first-order shear deformation theory with von Kármán kinematic nonlinearity. The material properties are considered to vary across thickness direction according to power law distribution. The electric potential is considered to be quadratic through thickness direction. Due to bifurcation analysis, the prebuckling deformation is initially investigated; then, in the case of simply supported edge condition, the buckling response of a bimorph functionally graded piezoelectric nanotube is studied and the influences of various parameters on buckling pressure are illustrated.

Protein microtubules (MTs) are one of the important intercellular components and have a vital role in the stability and strength of the cells. Due to applied external loads, protein microtubules may be involved buckling phenomenon. Due to impact of protein microtubules in cell reactions, it is important to determine their critical buckling load. Considering nature of protein microtubules, various parameters are effective on microtubules buckling. The small size of microtubules and also lack of uniformity of MTs properties in different directions caused the necessity of accuracy in the analysis of these bio-structure. In fact, microtubules must be considered as a size dependent cylinder, which behave as an orthotropic material. Hence, in the present work using first-order shear deformation model (FSDT), the buckling equations of anisotropic MTs are derived based on new modified couple stress theory (NMCST). After solving the stability equations, the influences of various parameters are measured on the MTs critical buckling load.

The present paper is concerned with the applicability of nonlocal strain gradient theory for axial buckling analysis of nanotubes. The first order shear deformation theory with the von Karman geometrical nonlinearity is utilized to establish theoretical formulations. The governing equations and boundary conditions are derived using the minimum potential energy principle. As main purpose of this study, the small length scale parameters are calibrated for the axial buckling problem of carbon nanotubes (CNTs) using molecular dynamics (MDs) simulations. Further the influences of different geometrical and material parameters, such as length and thickness ratio as well as small length scale parameters on the buckling response of nanotubes are studied. It is indicated that the effect of small length scale parameters on the critical buckling load becomes more prominent by increasing thickness and decreasing length ratio. Moreover, the calibrated small length scale parameters presented herein would be useful for the purpose of applying the nonlocal strain gradient theory for the analysis of nanotubes. The calibrated nonlocal strain gradient theory presented herein should be useful for researchers who are using the nonlocal strain gradient shell theories for analysis of micro/nanotubes.