• Steel and Composite Structures
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• 제29권1호
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• pp.53-66
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• 2018

A high-order nonlocal strain gradient model is developed for wave propagation analysis of porous FG nanoplates resting on a gradient hybrid foundation in thermal environment, for the first time. Material properties are assumed to be temperature-dependent and graded in the nanoplate thickness direction. To consider the thermal effects, uniform, linear, nonlinear, exponential, and sinusoidal temperature distributions are considered for temperature-dependent FG material properties. On the basis of the refined-higher order shear deformation plate theory (R-HSDT) in conjunction with the bi-Helmholtz nonlocal strain gradient theory (B-H NSGT), Hamilton's principle is used to derive the equations of wave motion. Then the dispersion relation between frequency and wave number is solved analytically. The influences of various parameters (such as temperature rise, volume fraction index, porosity volume fraction, lower and higher order nonlocal parameters, material characteristic parameter, foundations components, and wave number) on the wave propagation behaviors of porous FG nanoplates are investigated in detail.

• Advances in nano research
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• 제1권1호
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• pp.1-11
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• 2013

The thermal buckling properties of double-walled carbon nanotubes (DWCNTs) are studied using nonlocal Timoshenko beam model, including the effects of transverse shear deformation and rotary inertia. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. The geometric nonlinearity is taken into account, which arises from the mid-plane stretching. Considering the small-scale effects, the governing equilibrium equations are derived and the critical buckling temperatures under uniform temperature rise are obtained. The results show that the critical buckling temperature can be overestimated by the local beam model if the nonlocal effect is overlooked for long nanotubes. In addition, the effect of shear deformation and rotary inertia on the buckling temperature is more obvious for the higher-order modes. The investigation of the thermal buckling properties of DWCNTs may be used as a useful reference for the application and the design of nanostructures in which DWCNTs act as basic elements.

• International Journal of Aeronautical and Space Sciences
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• 제18권2호
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• pp.255-269
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• 2017

Free vibration analysis is presented for a simply-supported, functionally graded piezoelectric (FGP) nanobeam embedded on elastic foundation in the framework of third order parabolic shear deformation beam theory. Effective electro-mechanical properties of FGP nanobeam are supposed to be variable throughout the thickness based on power-law model. To incorporate the small size effects into the local model, Eringen's nonlocal elasticity theory is adopted. Analytical solution is implemented to solve the size-dependent buckling analysis of FGP nanobeams based upon a higher order shear deformation beam theory where coupled equations obtained using Hamilton's principle exist for such beams. Some numerical results for natural frequencies of the FGP nanobeams are prepared, which include the influences of elastic coefficients of foundation, electric voltage, material and geometrical parameters and mode number. This study is motivated by the absence of articles in the technical literature and provides beneficial results for accurate FGP structures design.

• Advances in nano research
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• 제6권3호
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• pp.279-298
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• 2018

Present investigation deals with the free vibration characteristics of nanoscale-beams resting on elastic Pasternak's foundation based on nonlocal strain-gradient theory and a higher order hyperbolic beam model which captures shear deformation effect without using any shear correction factor. The nanobeam is lying on two-parameters elastic foundation consist of lower spring layers as well as a shear layer. Nonlocal strain gradient theory takes into account two scale parameters for modeling the small size effects of nanostructures more accurately. Hamilton's principal is utilized to derive the governing equations of embedded strain gradient nanobeam and, after that, analytical solutions are provided for simply supported conditions to solve the governing equations. The obtained results are compared with those predicted by the previous articles available in literature. Finally, the impacts of nonlocal parameter, length scale parameter, slenderness ratio, elastic medium, on vibration frequencies of nanosize beams are all evaluated.

• Advances in nano research
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• 제8권4호
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• pp.265-276
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• 2020

A study that primarily focuses on nonlocal strain gradient plate model for the sole purpose of vibration examination, for graphene sheets under linearly variable in-plane mechanical loads. To study a better or more precise examination on graphene sheets, a new advance model was conducted which carries two scale parameters that happen to be related to the nonlocal as well as the strain gradient influences. Through the usage of two-variable shear deformation plate approach, that does not require the inclusion of shear correction factors, the graphene sheet is designed. Based on Hamilton's principle, fundamental expressions in regard to a nonlocal strain gradient graphene sheet on elastic half-space is originated. A Galerkin's technique is applied to resolve the fundamental expressions for distinct boundary conditions. Influence of distinct factors which can be in-plane loading, length scale parameter, load factor, elastic foundation, boundary conditions, and nonlocal parameter on vibration properties of the graphene sheets then undergo investigation.

• Advances in nano research
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• 제14권5호
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• pp.475-493
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• 2023

In the context of nonclassical nonlocal strain gradient elasticity, this article studies the free and forced responses of functionally graded material (FGM) porous nanoplates exposed to thermal and magnetic fields under a moving load. The developed mathematical model includes shear deformation, size-scale, miscorstructure influences in the framework of higher order shear deformation theory (HSDT) and nonlocal strain gradient theory (NSGT), respectively. To explore the porosity effect, the study considers four different porosity models across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The system of quations of motion of the FGM porous nanoplate, including the effects of thermal load, Lorentz force, due to the magnetic field and moving load, are derived using the Hamilton's principle, and then solved analytically by employing the Navier method. For the free and forced responses of the nanoplate, the effects of nonlocal elasticity, strain gradient elasticity, temperature rise, magnetic field intensity, porosity volume fraction, and porosity distribution are analyzed. It is found that the forced vibrations of FGM porous nanoplates under thermal and live loads can be damped by applying a directed magnetic field.

• Steel and Composite Structures
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• 제43권5호
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• pp.639-660
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• 2022

The bending and buckling behaviours of FG-GRNC laminated sandwich plates are investigated by using novel five-variables quasi 3D higher order shear deformation plate theory by considering the modified continuum nonlocal strain gradient theory. To calculate the effective Young's modulus of the GRNC sandwich plate along the thickness direction, and Poisson's ratio and mass density, the modified Halpin-Tsai model and the rule of the mixture are employed. Based on a new field of displacement, governing equilibrium equations of the GRNC sandwich plate are solved using a developed approach of Galerkin method. A detailed parametric analysis is carried out to highlight the influences of length scale and material scale parameters, GPLs distribution pattern, the weight fraction of GPLs, geometry and size of GPLs, the geometry of the sandwich plate and the total number of layers on the stresses, deformation and critical buckling loads. Some details are studied exclusively for the first time, such as stresses and the nonlocality effect.

• Steel and Composite Structures
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• 제30권6호
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• pp.517-534
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• 2019

In this paper, the effects of inevitable out-of-plane defects on the postbuckling behavior of single-layered graphene sheets (SLGSs) under in-plane loadings are investigated based on nonlocal first order shear deformation theory (FSDT) and von-Karman nonlinear model. A generic imperfection function, which takes the form of the products of hyperbolic and trigonometric functions, is employed to model out-of-plane defects as initial geometrical imperfections of SLGSs. Nonlinear equilibrium equations are derived from the principle of virtual work and variational formulation. The postbuckling equilibrium paths of imperfect graphene sheets (GSs) are presented by solving the governing equations via isogeometric analysis (IGA) and Newton-Raphson iterative method. Finally, the sensitivity of the postbuckling behavior of GS to shape, amplitude, extension on the surface, and location of initial imperfection is studied. Results showed that the small scale and initial imperfection effects on the postbuckling behavior of defective SLGS are important and cannot be ignored.

• Steel and Composite Structures
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• 제32권2호
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• pp.281-292
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• 2019

Nonlocal elasticity and Reddy plant theory are used to study the vibration response of functionally graded (FG) nanoplates resting on two parameters elastic medium called Pasternak foundation. Nonlocal higher order theory accounts for the effects of both scale and the effect of transverse shear deformation, which becomes significant where stocky and short nanoplates are concerned. It is assumed that the properties of FG nanoplate follow a power law through the thickness. In addition, Poisson's ratio is assumed to be constant in this model. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction of nanoplate with surrounding elastic medium. Using Hamilton's principle, size-dependent governing differential equations of motion and corresponding boundary conditions are derived. A differential quadrature approach is being utilized to discretize the model and obtain numerical solutions for various boundary conditions. The model is validated by comparing the results with other published results.

• Structural Engineering and Mechanics
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• 제69권4호
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• pp.439-455
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• 2019

This research deals with thermo-electro-mechanical buckling analysis of the sandwich nano-beams with face-sheets made of functionally graded carbon nano-tubes reinforcement composite (FG-CNTRC) based on the nonlocal strain gradient elasticity theory (NSGET) considering various higher-order shear deformation beam theories (HSDBT). The sandwich nano-beam with FG-CNTRC face-sheets is subjected to thermal and electrical loads while is resting on Pasternak's foundation. It is assumed that the material properties of the face-sheets change continuously along the thickness direction according to different patterns for CNTs distribution. In order to include coupling of strain and electrical field in equation of motion, the nonlocal non-classical nano-beam model contains piezoelectric effect. The governing equations of motion are derived using Hamilton principle based on HSDBTs and NSGET. The differential quadrature method (DQM) is used to calculate the mechanical buckling loads of sandwich nano-beam as well as critical voltage and temperature rising. After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various HSDBTs, length scale parameter (strain gradient parameter), the nonlocal parameter, the CNTs volume fraction, Pasternak's foundation coefficients, various boundary conditions, the CNTs efficiency parameter and geometric dimensions on the buckling behaviors of FG sandwich nano-beam. The numerical results indicate that, the amounts of the mechanical critical load calculated by PSDBT and TSDBT approximately have same values as well as ESDBT and ASDBT. Also, it is worthy noted that buckling load calculated by aforementioned theories is nearly smaller than buckling load estimated by FSDBT. Also, similar aforementioned structure is used to building the nano/micro oscillators.