Element Free Galerkin Method for Static Analysis of Thin Micro/Nanoscale Plates based on the Nonlocal Plate Theory

Naderi, A.; Baradaran, Gholam Hossein

doi:10.5829/idosi.ije.2013.26.07a.14

Cited by 8 publications

(6 citation statements)

References 32 publications

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“…Also, since the integral form of the nonlocal constitutive relations leads to a set of integropartial differential equations which are difficult to solve, some equivalent differential forms have been presented for that integral form. 1,2 Recently, an equivalent differential form has been applied progressively for mechanical analyses of nanostructures which are not really infinite bodies (see, for example, the previous studies 3–25 ).…”

Section: Introductionmentioning

confidence: 99%

Common nonlocal elastic constitutive relation and material-behavior modeling of nanostructures

Naderi

Saidi

2017

Proceedings of the Institution of Mechanical Engineers, Part N:

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This article reviews conventional nonlocal elasticity constitutive relation which is frequently used for mechanical analyses of nanostructures. It is shown here that since this constitutive relation has been essentially derived based on infinitebody assumption, it cannot consider the nonlocal effects at all points of a nanoscale body accurately. Also, it is shown that although the nonlocal constitutive relations can potentially consider the surface effects, that constitutive relation has been obtained substantially by ignoring those effects. So, it cannot also consider the surface effects accurately. Therefore, the conventional nonlocal constitutive relation generally is not accurate for material-behavior modeling and consequently mechanical analysis of nanostructures. Furthermore, common nonlocal constitutive law is examined in buckling problem of Timoshenko beam-columns to show another limitation of that constitutive law. Finally, some special cases for which that constitutive relation can be used more accurately are proposed.

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Section: Introductionmentioning

confidence: 99%

Common nonlocal elastic constitutive relation and material-behavior modeling of nanostructures

Naderi

Saidi

2017

Proceedings of the Institution of Mechanical Engineers, Part N:

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“…Calculation of the residual values: Convergence is fundamentally dependent on the response equilibrium between two overlapping domains. In order to satisfy Equation (11) and reach convergence, the interfacial residual norm should be minimized. 4.…”

Section: Solution On Local Domainmentioning

confidence: 99%

“…Another alternative is to employ multi-scale techniques [9] such as the micro/macro strategy [10], [11] or nonlinear localization techniques [12,13]. Also the coupling techniques such as Implicit Direct Coupling Approach (IDCA) [14,15],and Explicit Iterative Coupling Approach (EICA) [16] are the choice.…”

Section: Introductionmentioning

confidence: 99%

Coupling Nonlinear Element Free Galerkin and Linear Galerkin Finite Volume Solver for 2D Modeling of Local Plasticity in Structural Material

2020

IJE

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“…Substituting the Hamiltonian operator and equation (12) into equation 7, current density can be obtained as…”

Section: Maxwell's Relationsmentioning

confidence: 99%

“…They modelled a nanoparticle with a concentrated micro-mass at any position of simply supported rectangular nanoplate and showed that the results tend to the classical model in the absence of the nonlocal parameter. By introducing element-free Galerkin method, Naderi and Baradaran 12 carried out static analysis of thin orthotropic micro/nanoscale plates based on the nonlocal Kirchhoff plate theory. Also, they utilized the penalty method to apply the various boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Orthotropic patterns of visco-Pasternak foundation in nonlocal vibration of orthotropic graphene sheet under thermo-magnetic fields based on new first-order shear deformation theory

Amir

2016

Proceedings of the Institution of Mechanical Engineers, Part L:

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In the present research, vibration and instability of orthotropic graphene sheet subjected to thermo-magnetic fields are investigated. Orthotropic visco-Pasternak foundation is considered to analyze the influences of orthotropy angle, damping coefficient, normal and shear modulus. New first-order shear deformation theory is utilized due to accuracy of its polynomial functions compared to other theories of plate. Motion equations are obtained by means of Hamilton's principle and then solved analytically. Influences of various parameters such as small scale, magnetic field, orthotropic viscoelastic surrounding medium, thickness and aspect ratio of single layer graphene sheet on the vibration characteristics of nanoplate are discussed in detail. The results indicate that the stability of single layer graphene sheet is strongly dependent on applied magnetic field. Therefore, the mechanical behavior of single layer graphene sheet can be improved by applying magnetic field. The results of this investigation can be used in design and manufacturing of micro/nano mechanical systems.

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Element Free Galerkin Method for Static Analysis of Thin Micro/Nanoscale Plates based on the Nonlocal Plate Theory

Cited by 8 publications

References 32 publications

Common nonlocal elastic constitutive relation and material-behavior modeling of nanostructures

Common nonlocal elastic constitutive relation and material-behavior modeling of nanostructures

Coupling Nonlinear Element Free Galerkin and Linear Galerkin Finite Volume Solver for 2D Modeling of Local Plasticity in Structural Material

Orthotropic patterns of visco-Pasternak foundation in nonlocal vibration of orthotropic graphene sheet under thermo-magnetic fields based on new first-order shear deformation theory

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