Comments on nonlocal effects in nano-cantilever beams

Li, Cheng; Yao, Lin‐Quan; Chen, Weiqiu; Li, Shuang

doi:10.1016/j.ijengsci.2014.11.006

Cited by 246 publications

(82 citation statements)

References 42 publications

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“…the displacements of the Eringen nonlocal model are typically higher than their local counterpart, while the frequencies are generally lower. However, the study by and Li, Yao, Chen, and Li (2015) showed that the behavior of the Eringen nonlocal model as compared to the corresponding local counterpart depends upon the type of loading and boundary conditions. Although the stiffness may increase in some cases, there exists some cases where it has a softening effect (Li et al, 2015;.…”

Section: Clamped Vs Simply Supported Beammentioning

confidence: 99%

A unified integro-differential nonlocal model

Khodabakhshi

Reddy

2015

International Journal of Engineering Science

189

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a b s t r a c tIn this paper a unified integro-differential nonlocal elasticity model is presented and its use in the bending analysis of Euler-Bernoulli beams is illustrated. A general (for an elastic continuum) finite element formulation for the two-phase integro-differential form of Eringen nonlocal model is provided. The equations are specialized for the case of the Euler-Bernoulli beam theory. Several numerical examples, including the paradoxical cantilever beam problem that eluded other researchers, are provided to show how the present nonlocal model affects the transverse displacement of beams. The examples show that Eringen nonlocal constitutive relation has a softening effect on the beam, except for the case of the simply supported beam. A brief discussion on the applicability of the integro-differential model to other problems is also presented. Finally, the transition from the stiffened nonlocal simply supported beam to the softened nonlocal clamped beam is also investigated.

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Section: Clamped Vs Simply Supported Beammentioning

confidence: 99%

A unified integro-differential nonlocal model

Khodabakhshi

Reddy

2015

International Journal of Engineering Science

189

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“…Challamel et al (2014) presented an analytical method to calibrate the nonlocal parameter for buckling analysis of micro-structures. However, it was reported that the capability of nonlocal elasticity theory provided to study the size-dependent effects on the mechanical properties of small-scaled structures may exist some limited problems (Eltaher, Hamed, Sadoun, & Mansour, 2014;Li, Yao, Chen, & Li, 2015a;Lim, Zhang, & Reddy, 2015;Ma, Gao, & Reddy, 2008). There is an unresolved paradox that bending solutions of nonlocal nanobeams in some cases were found to be identical to the classical local solution, i.e., the small scale effect cannot be observed at all (Challamel & Wang 2008).…”

Section: Introductionmentioning

confidence: 99%

Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory

2015

International Journal of Engineering Science

306

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“…Recently, several studies focusing on the bending behavior of cantilevered beams have produced insubstantial results [57,58]. Benvenuti and Simone [59] presented the equivalence between the nonlocal and the gradient elasticity models by making reference to one-dimensional boundary value problems equipped with two integral stress-strain laws proposed by Eringen.…”

Section: Introductionmentioning

confidence: 99%

Postbuckling and Free Vibration of Multilayer Imperfect Nanobeams under a Pre-Stress Load

et al. 2018

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This paper investigates the postbuckling and free vibration response of geometrically imperfect multilayer nanobeams. The beam is assumed to be subjected to a pre-stress compressive load due to the manufacturing and its ends are kept at a fixed distance in space. The small-size effect is modeled according to the nonlocal elasticity differential model of Eringen within the nonlinear Bernoulli-Euler beam theory. The constitutive equations relating the stress resultants to the cross-section stiffness constants for a nonlocal multilayer beam are developed. The governing nonlinear equation of motion is derived and then manipulated to be given in terms of only the lateral displacement. The static problem is solved for the buckling load and the postbuckling deflection in terms of three parameters: Imperfection amplitude, size, and lamination. A closed-form solution for the buckling load in terms of all of the beam parameters is developed. With the presence of imperfection and size effects, it has been shown that the buckling load can be either less or greater than the Euler buckling load. Moreover, the free vibration in the pre and postbuckling domains are investigated for the first five modes. Numerical results show that the effects of imperfection, the nonlocal parameter, and layup on buckling loads and natural frequencies of the nanobeams are significant.

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Comments on nonlocal effects in nano-cantilever beams

Cited by 246 publications

References 42 publications

A unified integro-differential nonlocal model

A unified integro-differential nonlocal model

Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory

Postbuckling and Free Vibration of Multilayer Imperfect Nanobeams under a Pre-Stress Load

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