Dynamics of two-dimensional functionally graded tapered Timoshenko nanobeam in thermal environment using nonlocal strain gradient theory

Karami, Behrouz; Janghorban, Maziar; Rabczuk, Timon

doi:10.1016/j.compositesb.2019.107622

Cited by 104 publications

(28 citation statements)

References 51 publications

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“…In [ 26 ], the second strain gradient of Mindlin merged successfully with the nonlocal theory of Eringen. This model (NSGT) was incorporated in a lot of research performed on the nanoparticles in recent years—see e.g., [ 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 ] and many others—and can be a proper item at the nanoscale.…”

Section: Mathematical Modelmentioning

confidence: 99%

On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution

Malikan

Eremeyev

2020

Nanomaterials

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Among various magneto-elastic phenomena, flexomagnetic (FM) coupling can be defined as a dependence between strain gradient and magnetic polarization and, contrariwise, elastic strain and magnetic field gradient. This feature is a higher-order one than piezomagnetic, which is the magnetic response to strain. At the nanoscale, where large strain gradients are expected, the FM effect is significant and could be even dominant. In this article, we develop a model of a simultaneously coupled piezomagnetic–flexomagnetic nanosized Euler–Bernoulli beam and solve the corresponding problems. In order to evaluate the FM on the nanoscale, the well-known nonlocal model of strain gradient (NSGT) is implemented, by which the nanosize beam can be transferred into a continuum framework. To access the equations of nonlinear bending, we use the variational formulation. Converting the nonlinear system of differential equations into algebraic ones makes the solution simpler. This is performed by the Galerkin weighted residual method (GWRM) for three conditions of ends, that is to say clamp, free, and pinned (simply supported). Then, the system of nonlinear algebraic equations is solved on the basis of the Newton–Raphson iteration technique (NRT) which brings about numerical values of nonlinear deflections. We discovered that the FM effect causes the reduction in deflections in the piezo-flexomagnetic nanobeam.

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Section: Mathematical Modelmentioning

confidence: 99%

On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution

Malikan

Eremeyev

2020

Nanomaterials

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“…Hence, on the basis of Equations (29)- (31), Equations (19)-(21) can be expanded as [54][55][56][57][58][59][60][61] 1…”

Section: The Piezo-flexomagnetic Beam Modelmentioning

confidence: 99%

Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed Piezomagnetic Nanobeams

2020

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We investigated the stability of an axially loaded Euler–Bernoulli porous nanobeam considering the flexomagnetic material properties. The flexomagneticity relates to the magnetization with strain gradients. Here we assume both piezomagnetic and flexomagnetic phenomena are coupled simultaneously with elastic relations in an inverse magnetization. Similar to flexoelectricity, the flexomagneticity is a size-dependent property. Therefore, its effect is more pronounced at small scales. We merge the stability equation with a nonlocal model of the strain gradient elasticity. The Navier sinusoidal transverse deflection is employed to attain the critical buckling load. Furthermore, different types of axial symmetric and asymmetric porosity distributions are studied. It was revealed that regardless of the high magnetic field, one can realize the flexomagnetic effect at a small scale. We demonstrate as well that for the larger thicknesses a difference between responses of piezomagnetic and piezo-flexomagnetic nanobeams would not be significant.

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“…The motivation of the present paper is to extend the analysis on the hygro-thermal bending behavior of porous FG nano-beams, developed in [ 46 ] by using the aforementioned consistent nonlocal gradient formulations, to their dynamic response, against of many articles on the topic in which the hygro-thermal effects on the size-dependent behavior of nanostructures have been analyzed by making recourse to Eringen’s nonlocal model [ 47 , 48 , 49 , 50 , 51 , 52 , 53 ] or Lim’s nonlocal strain gradient theory in [ 54 , 55 , 56 ], more popularities due to their simply differential formulation.…”

Section: Introductionmentioning

confidence: 99%

Hygro-Thermal Vibrations of Porous FG Nano-Beams Based on Local/Nonlocal Stress Gradient Theory of Elasticity

et al. 2021

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In this manuscript the dynamic response of porous functionally-graded (FG) Bernoulli–Euler nano-beams subjected to hygro-thermal environments is investigated by the local/nonlocal stress gradient theory of elasticity. In particular, the influence of several parameters on both the thermo-elastic material properties and the structural response of the FG nano-beams, such as material gradient index, porosity volume fraction, nonlocal parameter, gradient length parameter, mixture parameter is examined. It is shown how the proposed approach is able to capture the dynamic behavior of porous functionally graded Bernoulli–Euler nano-beams under hygro-thermal loads and leads to well-posed structural problems of nano-mechanics.

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Dynamics of two-dimensional functionally graded tapered Timoshenko nanobeam in thermal environment using nonlocal strain gradient theory

Cited by 104 publications

References 51 publications

On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution

On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution

Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed Piezomagnetic Nanobeams

Hygro-Thermal Vibrations of Porous FG Nano-Beams Based on Local/Nonlocal Stress Gradient Theory of Elasticity

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