• Advances in concrete construction
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• v.15 no.2
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• pp.97-114
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• 2023

The nonlocal strain gradient theory for the static bending analysis of graphene nanoplatelets (GPLs) reinforced the nanoplate is developed in this paper. The nanoplatelet is exposed to thermo-mechanical loads and is also supposed to stand on an elastic foundation. For computing impressive composite material characteristics, the Halpin-Tsai model is selected for various sectors. The various distributions are propounded including UD, FG-O, and FG-X. The represented equations are acquired based on the virtual work and sinusoidal shear and normal deformation theory (SSNDT). Navier's solution as the analytical method is applied to solve these equations. Furthermore, the effects of GPL weight fraction, temperature parameters, distribution pattern and parameters of the foundation are presented and discussed.

• Advances in nano research
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• v.7 no.3
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• pp.191-208
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• 2019

In the present work the dynamic analysis of the functionally graded rectangular nanoplates is studied. The theory of nonlocal elasticity based on the quasi 3D high shear deformation theory (quasi 3D HSDT) has been employed to determine the natural frequencies of the nanosize FG plate. In HSDT a cubic function is employed in terms of thickness coordinate to introduce the influence of transverse shear deformation and stretching thickness. The theory of nonlocal elasticity is utilized to examine the impact of the small scale on the natural frequency of the FG rectangular nanoplate. The equations of motion are deduced by implementing Hamilton's principle. To demonstrate the accuracy of the proposed method, the calculated results in specific cases are compared and examined with available results in the literature and a good agreement is observed. Finally, the influence of the various parameters such as the nonlocal coefficient, the material indexes, the aspect ratio, and the thickness to length ratio on the dynamic properties of the FG nanoplates is illustrated and discussed in detail.

• Advances in aircraft and spacecraft science
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• v.5 no.5
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• pp.515-531
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• 2018

In this manuscript, buckling response of the functionally graded material (FGM) nanoplate is investigated. Two opposite edges of nanoplate is under linear and nonlinear varying normal stresses. The small-scale effect is considered by Eringen's nonlocal theory. Governing equation are derived by nonlocal theory and Hamilton's principle. Navier's method is used to solve governing equation in simply boundary conditions. The obtained results exactly match the available results in the literature. The results of this research show the important role of nonlocal effect in buckling and stability behavior of nanoplates. In order to study the FG-index effect and different loading condition effects on buckling of rectangular nanoplate, Navier's method is applied and results are presented in various figures and tables.

• Coupled systems mechanics
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• v.9 no.3
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• pp.201-217
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• 2020

This paper employs differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT) for studying free vibrational characteristics of porous functionally graded (FG) nanoplates coupled by visco-elastic foundation. A secant function based refined plate theory is used for mathematical modeling of the nano-size plate. Two scale factors are included in the formulation for describing size influences based on NSGT. The material properties for FG plate are porosity-dependent and defined employing a modified power-law form. Visco-elastic foundation is presented based on three factors including a viscous layer and two elastic layers.The governing equations achieved by Hamilton's principle are solved implementing DQM. The nanoplate vibration is shown to be affected by porosity, temperature rise,scale factors and viscous damping.

• Advances in aircraft and spacecraft science
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• v.7 no.2
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• pp.169-186
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• 2020

Based upon differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT), mechanical-hygro-thermal vibrational analyzes of shear deformable porous functionally graded (FG) nanoplate on visco-elastic medium has been performed. The presented formulation incorporates two scale factors for examining vibrational behaviors of nano-dimension plates more accurately. The material properties for FG plate are porosity-dependent and defined employing a modified power-law form. It is supposed that the nano-size plate is exposed to hygro-thermal and variable compressive mechanical loadings. The governing equations achieved by Hamilton's principle are solved implementing DQM. Presented results indicate the prominence of moisture/temperature variation, damping factor, material gradient index, nonlocal coefficient, strain gradient coefficient and porosities on vibrational frequencies of FG nano-size plate.

• Advances in nano research
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• v.7 no.1
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• pp.63-75
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• 2019

This article represents a quasi-3D theory for the buckling investigation of magneto-electro-elastic functionally graded (MEE-FG) nanoplates. All the effects of shear deformation and thickness stretching are considered within the presented theory. Magneto-electro-elastic material properties are considered to be graded in thickness direction employing power-law distribution. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of such nanoplates. Using Hamilton's principle, the nonlocal governing equations based on quasi-3D plate theory are obtained for the buckling analysis of MEE-FG nanoplates including size effect and they are solved applying analytical solution. It is found that magnetic potential, electric voltage, boundary conditions, nonlocal parameter, power-law index and plate geometrical parameters have significant effects on critical buckling loads of MEE-FG nanoscale plates.

• Smart Structures and Systems
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• v.19 no.6
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• pp.601-614
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• 2017

In this work, free vibration analysis of size-dependent functionally graded (FG) nanoplates resting on two-parameter elastic foundation is investigated based on a novel nonlocal refined trigonometric shear deformation theory for the first time. This theory includes undetermined integral variables and contains only four unknowns, with is even less than the conventional first shear deformation theory (FSDT). Mori-Tanaka model is employed to describe gradually distribution of material properties along the plate thickness. Size-dependency of nanosize FG plate is captured via the nonlocal elasticity theory of Eringen. By implementing Hamilton's principle the equations of motion are obtained for a refined four-variable shear deformation plate theory and then solved analytically. To show the accuracy of the present theory, our research results in specific cases are compared with available results in the literature and a good agreement will be demonstrated. Finally, the influence of various parameters such as nonlocal parameter, power law indexes, elastic foundation parameters, aspect ratio, and the thickness ratio on the non-dimensional frequency of rectangular FG nanoscale plates are presented and discussed in detail.

• Advances in nano research
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• v.7 no.4
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• pp.277-292
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• 2019

In this present paper, a new two dimensional (2D) and quasi three dimensional (quasi-3D) nonlocal shear deformation theories are formulated for free vibration analysis of size-dependent functionally graded (FG) nanoplates. The developed theories is based on new description of displacement field which includes undetermined integral terms, the issues in using this new proposition are to reduce the number of unknowns and governing equations and exploring the effects of both thickness stretching and size-dependency on free vibration analysis of functionally graded (FG) nanoplates. The nonlocal elasticity theory of Eringen is adopted to study the size effects of FG nanoplates. Governing equations are derived from Hamilton's principle. By using Navier's method, analytical solutions for free vibration analysis are obtained through the results of eigenvalue problem. Several numerical examples are presented and compared with those predicted by other theories, to demonstrate the accuracy and efficiency of developed theories and to investigate the size effects on predicting fundamental frequencies of size-dependent functionally graded (FG) nanoplates.

• Smart Structures and Systems
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• v.26 no.1
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• pp.77-87
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• 2020

By employing a quasi-3D plate formulation, the present research studies static stability of magneto-electro-thermo-elastic functional grading (METE-FG) nano-sized plates. Accordingly, influences of shear deformations as well as thickness stretching have been incorporated. The gradation of piezo-magnetic and elastic properties of the nano-sized plate have been described based on power-law functions. The size-dependent formulation for the nano-sized plate is provided in the context of nonlocal elasticity theory. The governing equations are established with the usage of Hamilton's rule and then analytically solved for diverse magnetic-electric intensities. Obtained findings demonstrate that buckling behavior of considered nanoplate relies on the variation of material exponent, electro-magnetic field, nonlocal coefficient and boundary conditions.

• Smart Structures and Systems
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• v.23 no.3
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• pp.215-225
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• 2019

In the present paper, the nonlocal strain gradient refined model is used to study the thermal stability of sandwich nanoplates integrated with piezoelectric layers for the first time. The influence of Kerr elastic foundation is also studied. The present model incorporates two small-scale coefficients to examine the size-dependent thermal stability response. Elastic properties of nanoplate made of functionally graded materials (FGMs) are supposed to vary through the thickness direction and are estimated employing a modified power-law rule in which the porosity with even type of distribution is approximated. The governing differential equations of embedded sandwich piezoelectric porous nanoplates under hygrothermal loading are derived through Hamilton's principle where the Galerkin method is applied to solve the stability problem of the nanoplates with simply-supported edges. It is indicated that the thermal stability characteristics of the porous nanoplates are obviously influenced by the porosity volume fraction and material variation, nonlocal parameter, strain gradient parameter, geometry of the nanoplate, external voltage, temperature and humidity variations, and elastic foundation parameters.