Buckling analysis of shear deformable nanorods within the framework of nonlocal elasticity theory

Xu, Shunfu; Wang, Chen; Xu, Mengrui

doi:10.1016/j.physe.2012.02.022

Cited by 10 publications

(5 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Rather than relying on the numerical simulation, Xu [47] independently investigated this problem theoretically with the help of the homotopy perturbation method. For stubby nanocolumns, Xu et al [48] exploited the Timoshenko hypothesis as a basis for the nonlinear postbuckling description, and in such a way the role of shear deformation in the postbuckling behavior was revealed. By using Pontryagin's maximum principle, the optimal shape of a nonlocal elastic rod clamped at both ends was determined by Atanackovic et al [49].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection

Wang

2013

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Investigated herein is the postbuckling behavior of an initially imperfect nonlocal elastic column, which is simply supported at one end and subjected to an axial force at the other movable end. The governing nonlinear differential equation of the axially loaded nonlocal elastic column experiencing large deflection is first established within the framework of Eringen's nonlocal elasticity theory in order to embrace the size effect. Its semianalytical solutions by the virtue of homotopy perturbation method, as well as the successive approximation algorithm, are determined in an explicit form, through which the postbuckling equilibrium loads in terms of the end rotation angle and the deformed configuration of the column at this end rotation are predicted. By comparing the degenerated results with the exact solutions available in the literature, the validity and accuracy of the proposed methods are numerically substantiated. The size effect, as well as the initial imperfection, on the buckled configuration and the postbuckling equilibrium path is also thoroughly discussed through parametric studies.

show abstract

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection

Wang

2013

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…There has been extensive research on the buckling of nanostructures, from the formulation of nonlocal models of EBT, TBT, and LBT beam theories to the nonlocal classical and shear deformation beam and plate theories using von Karman nonlinear strains [123,151,[191][192][193][194]. Few researchers studied the buckling behavior of nanobeams using nonlocal integral and two-phase nonlocal integral model of Eringen [138,195].…”

Section: Nonlocal Elasticity Theorymentioning

confidence: 99%

Advances in modelling and analysis of nano structures: a review

Chandel

Wang

Talha

2020

Nanotechnology Reviews

View full text Add to dashboard Cite

AbstractNanostructures are widely used in nano and micro-sized systems and devices such as biosensors, nano actuators, nano-probes, and nano-electro-mechanical systems. The complete understanding of the mechanical behavior of nanostructures is crucial for the design of nanodevices and systems. Therefore, the flexural, stability and vibration analysis of various nanostructures such as nanowires, nanotubes, nanobeams, nanoplates, graphene sheets and nanoshells has received a great attention in recent years. The focus has been made, to present the structural analysis of nanostructures under thermo-magneto-electro-mechanical loadings under various boundary and environmental conditions. This paper also provides an overview of analytical modeling methods, fabrication procedures, key challenges and future scopes of development in the direction of analysis of such structures, which will be helpful for appropriate design and analysis of nanodevices for the application in the various fields of nanotechnology.

show abstract

“…39into Eqs. (36) and 37gives Now, we shall use Ritz variational method (Lembo [39]). It is possible to integrate the above two equations and taking the variation with respect to the parameters W m and m .…”

Section: Buckling Of a Nanorodmentioning

confidence: 99%

“…Lim et al [35] investigated the thermal buckling of nanorods based on Eringen's nonlocal elasticity theory. Xu et al [36] considered the buckling and postbuckling responses of shear deformable nanorods by using a perturbation strategy. Barretta et al [37] studied the small-scale impacts in FG nanorods with the aid of nonlocal continuum mechanics.…”

Section: Introductionmentioning

confidence: 99%

A two-unknown nonlocal shear and normal deformations theory for buckling analysis of nanorods

Zenkour

2020

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

The present article presents a simple nonlocal two-unknown shear and normal deformation beam theory to discuss the buckling response of nanorods. The theory uses two variables only and takes under consideration the small-scale impact as well as the inclusion of both shear and normal deformations. The equilibrium equations and end conditions are gained utilizing the principle of virtual work. Different end conditions like pinned, clamped and free are studied. The critical buckling loads are obtained for axially loaded nanorods with different end conditions. The significant of small-scale, shear and normal deformation parameters are investigated. Some validation examples are presented, and the sensitivity of all parameters on the critical and other buckling loads of nanorods may be observed.

show abstract

Buckling analysis of shear deformable nanorods within the framework of nonlocal elasticity theory

Cited by 10 publications

References 30 publications

Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection

Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection

Advances in modelling and analysis of nano structures: a review

A two-unknown nonlocal shear and normal deformations theory for buckling analysis of nanorods

Contact Info

Product

Resources

About