• Steel and Composite Structures
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• v.32 no.2
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• pp.173-187
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• 2019

This study is concerned with the stability of laminated composite plates modelled using Eringen's nonlocal differential model (ENDM) and a novel refined-hyperbolic-shear-deformable plate theory. The plate is assumed to be lying on the Pasternak elastic foundation and is under the influence of an in-plane magnetic field. The governing equations and boundary conditions are obtained through Hamilton's principle. An analytical approach considering Navier series is used to fine the critical bucking load. After verifying with existing results for the reduced cases, the present model is then used to study buckling of the laminated composite plate. Numerical results demonstrate clearly for the first time the roles of size effects, magnetic field, foundation parameters, moduli ratio, geometry, lay-up numbers and sequences, fiber orientations, and boundary conditions. These results could be useful for designing better composites and can further serve as benchmarks for future studies on the laminated composite plates.

• 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.

• Advances in nano research
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• v.6 no.2
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• pp.113-133
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• 2018

In this work, free vibration characteristics of functionally graded piezoelectric (FGP) nanobeams based on third order parabolic shear deformation beam theory are studied by presenting a Navier type solution as the first attempt. Electro-mechanical properties of FGP nanobeam are supposed to change continuously throughout the thickness based on power-law model. To capture the small size effects, Eringen's nonlocal elasticity theory is adopted. Using Hamilton's principle, the nonlocal governing equations for third order shear deformable piezoelectric FG nanobeams are obtained and they are solved applying analytical solution. By presenting some numerical results, it is demonstrated that the suggested model presents accurate frequency results of the FGP nanobeams. The influences of several parameters including, external electric voltage, power-law exponent, nonlocal parameter and mode number on the natural frequencies of the size-dependent FGP nanobeams is discussed in detail.

• Advances in nano research
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• v.6 no.2
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• pp.93-112
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• 2018

An analytical solution of the buckling governing equations of functionally graded piezoelectric (FGP) nanobeams obtained by using a developed third-order shear deformation theory is presented. Electro-mechanical properties of FGP nanobeam are supposed to change continuously in the thickness direction based on power-law model. To capture the small size effects, Eringen's nonlocal elasticity theory is adopted. Employing Hamilton's principle, the nonlocal governing equations of a FG nanobeams made of piezoelectric materials are obtained and they are solved using Navier-type analytical solution. Results are provided to show the effect of different external electric voltage, power-law index, nonlocal parameter and slenderness ratio on the buckling loads of the size-dependent FGP nanobeams. The accuracy of the present model is verified by comparing it with nonlocal Timoshenko FG beams. So, this study makes the first attempt for analyzing buckling behavior of higher order shear deformable FGP nanobeams.

• Advances in nano research
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• v.9 no.2
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• pp.91-104
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• 2020

The bending, stability (buckling) and vibration response of nano sized beams is presented in this study based on the Eringen's nonlocal elasticity theory in conjunction with the Euler-Bernoulli beam theory. For this purpose, the bending, buckling and vibration problem of Euler-Bernoulli nanobeams are developed and solved on the basis of nonlocal elasticity theory. The effects of various parameters such as nonlocal parameter e₀a, length of beam L, mode number n, distributed load q and cross-section on the bending, buckling and vibration behaviors of carbon nanotubes idealized as Euler-Bernoulli nanobeam is investigated. The transverse deflections, maximum transverse deflections, vibrational frequency and buckling load values of carbon nanotubes are given in tables and graphs.

• Structural Engineering and Mechanics
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• v.60 no.4
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• pp.707-727
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• 2016

In this paper, thermal vibration of a nonlocal functionally graded (FG) plates with arbitrary boundary conditions under linear and non-linear temperature fields is explored by developing a refined shear deformation plate theory with an inverse cotangential function in which shear deformation effect was involved without the need for shear correction factors. The material properties of FG nanoplate are considered to be temperature-dependent and graded in the thickness direction according to the Mori-Tanaka model. On the basis of non-classical higher order plate model and Eringen's nonlocal elasticity theory, the small size influence was captured. Numerical examples show the importance of non-uniform thermal loadings, boundary conditions, gradient index, nonlocal parameter and aspect and side-to-thickness ratio on vibrational responses of size-dependent FG nanoplates.

• Advances in nano research
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• v.5 no.4
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• pp.313-336
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• 2017

This article investigates vibration behavior of magneto-electro-elastic functionally graded (MEE-FG) nanobeams embedded in two-parameter elastic foundation using a third-order parabolic shear deformation beam theory. Material properties of MEE-FG nanobeam are supposed to be variable throughout the thickness based on power-law model. Based on Eringen's nonlocal elasticity theory which captures the small size effects and using the Hamilton's principle, the nonlocal governing equations of motions are derived and then solved analytically. Then the influences of elastic foundation, magnetic potential, external electric voltage, nonlocal parameter, power-law index and slenderness ratio on the frequencies of the embedded MEE-FG nanobeams are studied.

• Structural Engineering and Mechanics
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• v.81 no.1
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• pp.29-37
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• 2022

The present paper deals with the application of one dimensional piezoelectric materials in particular piezo-thermoelastic nanobeam. The generalized piezo-thermo-elastic theory with two temperature and Euler Bernoulli theory with small scale effects using nonlocal Eringen's theory have been used to form the mathematical model. The ends of nanobeam are considered to be simply supported and at a constant temperature. The mathematical model so formed is solved to obtain the non-dimensional expressions for lateral deflection, electric potential, thermal moment, thermoelastic damping and frequency shift. Effect of frequency and nonlocal parameter on the lateral deflection, electric potential, thermal moment with generalized piezothermoelastic theory are represented graphically using the MATLAB software. Comparisons are made with the different theories of thermoelasticity.

• Structural Engineering and Mechanics
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• v.63 no.3
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• pp.401-415
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• 2017

In this article, hygro-thermo-mechanical vibration and buckling of exponentially graded (EG) nanoplates resting on two-parameter Pasternak foundations are studied using the four-unknown shear deformation plate theory. The material properties are presumed to change only in the thickness direction of the EG nanoplate according to two exponential laws distribution. The boundary conditions of the nanoplate may be simply supported, clamped, free or combination of them. To consider the small scale effect on forced frequencies and buckling, Eringen's differential form of nonlocal elasticity theory is employed. The accuracy of the present study is investigated considering the available solutions in literature. A detailed analysis is executed to study the influences of the plate aspect ratio, side-to-thickness ratio, temperature rise, moisture concentration and volume fraction distributions on the vibration and buckling of the nanoplates.

• Structural Engineering and Mechanics
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• v.68 no.1
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• pp.131-157
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• 2018

In this study, Eringen nonlocal elasticity theory in conjunction with surface elasticity theory is employed to study nonlinear free vibration behavior of FG nano-plate lying on elastic foundation, on the base of Reddy's plate theory. The material distribution is assumed as a power-law function and effective material properties are modeled using Mori-Tanaka homogenization scheme. Hamilton's principle is implemented to derive the governing equations which solved using DQ method. Finally, the effects of different factors on natural frequencies of the nano-plate under hygrothermal situation and various boundary conditions are studied.