Non-standard and constitutive boundary conditions in nonlocal strain gradient elasticity

Zaera, R.; Serrano, Óscar; Fernández-Sáez, J.

doi:10.1007/s11012-019-01122-z

Cited by 31 publications

(6 citation statements)

References 50 publications

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“…It is beneficial to point that as a diverse common continuum theory, the NSGT in differential state is yielded from the conversion of strain gradient, in integral form, to a differential equation, and it has been widely hired with neglecting imperative constitutive boundary conditions (CBCs) resulted from this transformation. According to this verifiable truth, the incongruity of the NSGT has been recently affirmed [86,87], so that it has been showed and proved that the order of the NSGT equations are less than the number of all imperative boundary conditions. Because of these uncertainties about the NSGT along with paradox of the differential state of nonlocal theory, in this paper, the two-phase local/nonlocal theory is appointed to take the size effects.…”

Section: Introductionmentioning

confidence: 89%

Size dependent effects of two phase viscoelastic medium on damping vibrations of smart nanobeams: an efficient implementation of GDQM

Naderi

Behdad

Fakher

2022

Smart Mater. Struct.

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This paper studies the dynamics of nonlocal piezo-magnetic nanobeams (PMNBs) embedded in the local/nonlocal ‎viscoelastic medium through the consistent and paradox-free model of the nonlocal theory. Besides, to perform the dynamic analysis, an exact solution and an efficient approach of Generalized Differential Quadrature Method (GDQM) are introduced. Since the size-dependency of the uniform loads is wrongly neglected by the nonlocal elasticity in differential form, the size-dependency of piezo-magnetic load is applied through the two-phase theory. Also, size dependency of the viscoelastic medium is accurately applied and examined through the solutions presented employing the differential two-phase theory and satisfying the constitutive boundary conditions. In this regard, the two-phase resultant equations of motions together with boundary conditions ‎including the constitutive ones related to two-phase ‎PMNB and the two-phase medium are attained. To confirm the credibility and efficiency of the extracted equations as well as presented solution ‎procedures, several analogical studies are accomplished, and it is shown that the results obtained from the differential relations are reliable and consistence with those extracted from the integral nonlocal relations. It is shown that the present approach of the GDQM simplifies the solution procedures of the nonlocal problems and improves the precisions in the cases close to the pure nonlocal state. The presented results emphasize that the size-dependency of viscoelastic medium, external electric, and magnetic loads play significant roles on the vibration ‎characteristics, and therefore it must be considered based on two-phase theory. The available results can be helpful to achieve an excellent design of smart nanobeams embedded in viscoelastic medium.

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Section: Introductionmentioning

confidence: 89%

Size dependent effects of two phase viscoelastic medium on damping vibrations of smart nanobeams: an efficient implementation of GDQM

Naderi

Behdad

Fakher

2022

Smart Mater. Struct.

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“…It was found that the bending, as well as shear components associated with the radial displacement, were considered as the increasing functions of the angle of the nanobeam. Nonlocal strain-gradient model behavior of nano-structures with consideration of non-standard as well as constitutive boundary conditions was scrutinized by Zaera et al [474]. They revealed that the obtained solution did not comply with energy conservation.…”

Section: Linear Static Bending Of Micro/nano-structuresmentioning

confidence: 99%

A review of size-dependent continuum mechanics models for micro- and nano-structures

Roudbari

Jorshari

et al. 2022

Thin-Walled Structures

115

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“…xx 1 are the classical and higher-order stresses, respectively. Based on Lim's theory, the final constitutive equation of the nonlocal strain-gradient model can be proposed as [69][70][71][72][73][74][75][76][77][78][79]:…”

Section: Nonlocal Strain-gradient Continuum Mechanics Theorymentioning

confidence: 99%

A Review on the Mechanical Behavior of Size-Dependent Beams and Plates using the Nonlocal Strain-Gradient Model

Jorshari

Roudbari

2021

J. Basic Appl. Sci.

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Nowadays, the mechanical characteristics of micro-/nano-structures in the various types of engineering disciplines are considered as remarkable criteria which may restrict the performance of small-scale structures in the reality for a certain application. This paper deals with a comprehensive review pertinent to using the nonlocal strain-gradient continuum mechanics model of size-dependent micro-/nano-beams/-plates. According to the non-classical features of materials, using size-dependent continuum mechanics theories is mandatory to investigate accurately the mechanical characteristics of the micro-/nano-structures. Recently, the number of researches related to the analysis of micro-/nano-structures with various geometry including beams as well as plates is considerable. In this regard, the mechanical behavior of these structures induced by different loadings such as vibration, wave propagation, and buckling behavior associated with the nonlocal strain-gradient continuum mechanics model is presented in this review work. Proposing the most valuable literature pertinent to the nonlocal strain-gradient continuum mechanics theory of micro-/nano-beams/plates is the main objective of this detailed survey.

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Non-standard and constitutive boundary conditions in nonlocal strain gradient elasticity

Cited by 31 publications

References 50 publications

Size dependent effects of two phase viscoelastic medium on damping vibrations of smart nanobeams: an efficient implementation of GDQM

Size dependent effects of two phase viscoelastic medium on damping vibrations of smart nanobeams: an efficient implementation of GDQM

A review of size-dependent continuum mechanics models for micro- and nano-structures

A Review on the Mechanical Behavior of Size-Dependent Beams and Plates using the Nonlocal Strain-Gradient Model

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