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Abstract
Research Subject: In recent years, the use of graphene nanoplatelets (GnPs) in polymer nanocomposites has attracted considerable attention. Dispersion state of GnPs in the polymer matrix has a great importance which can affect microstructure and final properties of nanocomposite. Therefore, in the present work, the effect of compatibilizer on the dispersion state of GnPs and also on internal structure, orientation, and tensile properties of polypropylene (PP)/GnPs nanocomposite fibers are investigated.
Research Approach: PP/GnPs nanocomposite fibers containing 0.1% and 0.5% GnPs with and without maleic anhydride-grafted polypropylene (PP-g-MA) were melt spun. Dispersion state and location of GnPs in the nanocomposite fibers were investigated by transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS). Fiber orientation and crystallinity were studied by polarized Fourier transform infrared (FTIR) spectroscopy and differential scanning calorimetry (DSC), respectively. Moreover, fracture behaviour of PP/GnPs nanocomposite fibers was investigated by cross-sectional scanning electron microscopy (SEM) images of tensile fractured samples. Using Halpin-Tsai model, experimental tensile moduli of fibers were compared with the predicted values. 
Main Results: TEM images show that in the compatibilized PP/MA/GnPs nanocomposite fibers, GnPs aggregates decrease and their size also reduces, suggesting that GnPs dispersion improved. An increase in L_p of the compatibilized sample recorded from SAXS analysis indicates that the more GnPs are located in the intrafibrillar region. Based on polarized FTIR and DSC results, orientation and crystallinity of PP/G0.5 nanocomposite fiber are found to significantly increase after inclusion of PP-g-MA. Moreover, reinforcing effect of GnPs in PP/MA/GnPs nanocomposite fibers could be explained by better GnPs dispersion and changes in internal structure of fiber. Furthermore, the tensile fracture behavior of PP/GnPs nanocomposite fiber changes from ductile to brittle in the presence of PP-g-MA.

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The present study proposes an analytical solution for the axisymmetric/asymmetric buckling analysis of thin circular/annular nanoplates under uniform radial compressive in-plane load. In order to consider small scale effects, nonlocal elasticity theory of Eringen is employed. To ensure the efficiency and stability of the present methodology, the results are compared with other presented in literature. Material properties including Young’s modulus, density, Poison’s ratio are assumed to be constant through the body of nanoplate. In addition, the effect of small scales on critical buckling loads for different parameters such as radius of the FG nanoplate, boundary condition, mode number and geometry parameters are investigated. In order to obtain the critical buckling load, the asymmetric modes as well as axisymmetric modes are considered. The thin nanoplate is modeled using Kirchhoff plate theory.

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In this paper, nonlinear bending of rectangular nanoplates of Graphene subjected to a transverse uniform load, with incorporation of the nonlocal effect of Eringen based on the first-order shear deformation theory (FSDT) of orthotropic plates and Von Karman nonlinear strains is investigated using differential quadrature method (DQM). In order to validate of the solution accuracy, the simplified results have been compared with results of two developed numerical solution methods and other available results. Comparisons show an excellent agreement between the results. Finally, effects of small scale parameter, aspect ratio, thickness of plate, load value, boundary conditions and efficacy of large deflection, on the maximum deflection and different deflections ratio for nonlocal theory of thin plate and nonlocal FSDT are investigated. Results reveal that among the considered parameters, just aspect of plate is the parameter of difference between two employed nonlocal theories and the small scale parameter has not any effect on the mentioned difference. Also, it is found that the small scale parameter has a noticeable effect on the decrease of deflection of nonlinear solution; so that, unlike the larger values of mechanical load, this parameter has less effect for long length of square plate.

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In this paper, nonlinear free vibration of a Nano plates rectangular has been investigated. For this purpose, first, the equations of motion for Nano plate which is considered as a continuous system have been derived using Hamilton principle based on classical plate theory. Then, by definition an stress function and using Galerkin method the equations converted to an ordinary nonlinear equation and a compatible equations. Using multiple time scale method this equation has been solved and analytical relations for first nonlinear natural frequency and nonlinear mode shaped have been derived. Then for example, these relations have been studied for Graphen sheet in Armchair and Zigzag structure and the effect of aspect ratio and nonlocal elasticity parameter on natural frequency have been investigated.

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In the present study the free vibration analysis of functionally graded rectangular nanoplates in thermal environment is investigated. The modified coupled stress theory based on the first order shear deformation theory has been used to obtain the natural frequencies of the nanoplate. Modified coupled stress theory is a non-classical theory. In this theory material length scale parameter is applied to capture the size effect of the microstructures which the earlier classical plate theories were not able to explain these effects. The functionally graded material properties are varied continuously and smoothly along the thickness. The Poisson’s ratio of the FGM plate is assumed to be constant in the whole plate. In order to validate the present method, the natural frequencies of the both functionally graded rectangular plate and rectangular nanoplates are compared with those are reported in the literature, separately. Finally, the effect of various parameters such as; the power law index, the thickness to length scale parameter ratio, aspect ratio, thickness ratio on the natural frequencies of plates in thermal environments with different temperatures are presented and discussed in detail.

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Conventional Ritz and Galerkin methods based on local theory of elasticity employ polynomials as their approximating functions, however these methods are not convenient to use in three-dimensional nonlocal analysis. In the present study, to conquer this difficulty, a type of weighted residual approach with a set of trigonometric approximating functions were developed. By using appropriate trigonometric approximating functions, it is possible to consider the effect of various edges boundary condition on frequency behavior of nanoplate. Validation of present formulation is carried out by comparing numerical result with the published results. It is concluded that the effect of nonlocal parameter on natural frequencies is significant especially in higher modes due to the lower wavelength of the mode. The research shows that in nonlocal elasticity there are distinct discrepancies between behaviors of two and three-dimensional results. In addition, the difference between the two- and three-dimensional results in local elasticity is not as noticeable as in nonlocal elasticity. Furthermore, the effects of length to thickness ratio, aspect ratio, nonlocal parameter and different boundary conditions on fundamental natural frequency of nanoplates were studied. This benchmark solution can be used to assess the accuracy of conventional two-dimensional theories.

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In this paper, the nonlocal buckling behavior of a biaxially loaded graphene sheet with piezoelectric layers based on an isotropic smart nanoplate model is studied. The equilibrium equations are derived with the von Karman-type geometrical nonlinearity by considering the small scale effect. The buckling of multilayer smart nanoplate made of graphene and piezoelectric materials in open circuit conditions is investigated. Based on the nonlocal elasticity and shear and normal deformation theories, the governing equilibrium equations are obtained using the principle of minimum total potential energy and Maxwell’s equation.
Using an analytical approach, the governing stability equations of smart nanoplate have been presented in terms of displacement components and electrical potential. In order to obtain the stability equations, the adjacent equilibrium criterion is used. The stability equations are then solved analytically, assuming simply supported boundary condition along all edges. To validate the results, the critical buckling load values have been compared with available resources. Finally, following validation of the results, numerical results for intelligent nanoplate are presented.
Also, the effects of different parameters such as nanoplate length, different nonlocal parameter, piezoelectric layers thickness, the graphene thickness to length ratio, the piezoelectric layer thickness to graphene thickness ratio and type of Piezoelectric material on the critical buckling loads of intelligent nanoplate are studied in detail. Furthermore, the effect of the mentioned parameters on the critical buckling loads have been presented in some figures.

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The present study investigates the surface energy of metallic nanoplates as the most basic thermodynamic concept of nanostructures using one of the most efficient available computational tools in the field of nanoscience i.e. the molecular dynamics simulations. Whenever physicochemical properties of nanostructures are discussed, the surface energy is one of the key parameters. This parameter has the utmost importance at nanoscale since at this scale the surface to volume ratio is very large and thus there is a significant difference between nanoscale properties and the engineering scale properties. In this study, the surface energy of gold and silver metallic nanoplates using molecular dynamics simulations are investigated and shown to be dependent on size. The surface energy of metallic nanoplates with different thicknesses were calculated and it was shown that for very thin metallic nanoplates with sufficiently small thickness in the order of a few nanometers, the surface energy is dependent on the thickness of nanoplate and the surface energy decreases by reducing the thickness of the nanoplate. By analyzing the excess energy of different layers in very thin nanoplates, it was found that this size-dependent behavior is due to the reduction of excess surface free energy density in surface layers and its increase in the inner layers that overall reduces the surface energy of nanoplate.