Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory

Nateghi, Alireza; Salamat‐talab, Mazaher; Rezapour, Javad; Daneshian, Behrouz

doi:10.1016/j.apm.2011.12.035

Cited by 186 publications

(34 citation statements)

References 35 publications

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“…In view of the difficulties in determining the material length scale parameters, Yang et al [7] proposed the modified couple stress theory in which only one length scale parameter is required. There have been a number of sizedependent models developed for FG beams based on the modified couple stress theory [8][9][10][11][12][13][14][15][16][17][18]. These size-dependent models adopted various beam theories such as EulerBernoulli beam theory (EBT) [8][9][10][11], Timoshenko beam theory (TBT) [9][10][12][13][14], and higher-order shear deformation beam theory (HBT) [10,[15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Size-dependent behavior of functionally graded sandwich microbeams based on the modified couple stress theory

Thai

Nguyen

et al. 2015

Composite Structures

113

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Northumbria University has developed Northumbria Research Link (NRL) to enable users to access the University's research output. Copyright © and moral rights for items on NRL are retained by the individual author(s) and/or other copyright owners. Single copies of full items can be reproduced, displayed or performed, and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided the authors, title and full bibliographic details are given, as well as a hyperlink and/or URL to the original metadata page. The content must not be changed in any way. Full items must not be sold commercially in any format or medium without formal permission of the copyright holder. The full policy is available online: http://nrl.northumbria.ac.uk/policies.html This document may differ from the final, published version of the research and has been made available online in accordance with publisher policies. To read and/or cite from the published version of the research, please visit the publisher's website (a subscription may be required.) Accepted ManuscriptSize-dependent behaviour of functionally graded sandwich microbeams based on the modified couple stress theory Huu-Tai Thai, Thuc P. Vo, Trung-Kien Nguyen, Jaehong Lee PII:S0263-8223 (14) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. The results reveals that the inclusion of the size effects results in an increase in the beam stiffness, and consequently, leads to a reduction of deflections and stresses and an increase in natural frequencies and critical buckling loads. Such effects are more pronounced when the beam depth was small, but they become negligible with the increase of the beam depth.

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Section: Introductionmentioning

confidence: 99%

Size-dependent behavior of functionally graded sandwich microbeams based on the modified couple stress theory

Thai

Nguyen

et al. 2015

Composite Structures

113

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“…The buckling analysis of functionally graded micro beams based on the MCST is presented in Nateghi et al [20]. The free vibration of a single-layered graphene sheet resting on an elastic matrix as a Pasternak foundation model explored by using the modified couple stress theory is presented by Bekir and Civalek [21].…”

Section: Introductionmentioning

confidence: 99%

Thermal Effect on Free Vibration and Buckling of a Double-Microbeam System

Atanasov¹,

Karličić²,

Kozić³

et al. 2017

FU Mech Eng

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“…Ansari et al [17][18][19] analyzed the size-dependent bending and thermal buckling and postbuckling of functionally graded Timoshenko microbeams based on a strain gradient elasticity theory. Nateghi et al [20] contributed to the field by examining the buckling response of functionally graded microbeams based on the modified couple stress theory. Akg€ oz and Civalek [21] investigated the buckling behavior of an axially forced microbeam employing both the modified couple stress and classical couple stress theories.…”

Section: Introductionmentioning

confidence: 99%

Coupled Nonlinear Dynamics of Geometrically Imperfect Shear Deformable Extensible Microbeams

Ghayesh

Farokhi

2015

Journal of Computational and Nonlinear Dynamics

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This paper aims at analyzing the coupled nonlinear dynamical behavior of geometrically imperfect shear deformable extensible microbeams based on the third-order shear deformation and modified couple stress theories. Using Hamilton's principle and taking into account extensibility, the three nonlinear coupled continuous expressions are obtained for an initially slightly curved (i.e., a geometrically imperfect) microbeam, describing the longitudinal, transverse, and rotational motions. A high-dimensional Galerkin scheme is employed, together with an assumed-mode technique, in order to truncate the continuous system with an infinite number of degrees of freedom into a discretized model with sufficient degrees of freedom. This high-dimensional discretized model is solved by means of the pseudo-arclength continuation technique for the system at the primary resonance, and also by direct time-integration to characterize the dynamic response at a fixed forcing amplitude and frequency; stability analysis is conducted via the Floquet theory. Apart from analyzing the nonlinear resonant response, the linear natural frequencies are obtained via an eigenvalue analysis. Results are shown through frequency-response curves, force-response curves, time traces, phase-plane portraits, and fast Fourier transforms (FFTs). The effect of taking into account the length-scale parameter on the coupled nonlinear dynamic response of the system is also highlighted. Coupled Nonlinear Dynamics of Geometrically Imperfect Shear Deformable Extensible MicrobeamsThis paper aims at analyzing the coupled nonlinear dynamical behavior of geometrically imperfect shear deformable extensible microbeams based on the third-order shear deformation and modified couple stress theories. Using Hamilton's principle and taking into account extensibility, the three nonlinear coupled continuous expressions are obtained for an initially slightly curved (i.e., a geometrically imperfect) microbeam, describing the longitudinal, transverse, and rotational motions. A high-dimensional Galerkin scheme is employed, together with an assumed-mode technique, in order to truncate the continuous system with an infinite number of degrees of freedom into a discretized model with sufficient degrees of freedom. This high-dimensional discretized model is solved by means of the pseudo-arclength continuation technique for the system at the primary resonance, and also by direct time-integration to characterize the dynamic response at a fixed forcing amplitude and frequency; stability analysis is conducted via the Floquet theory. Apart from analyzing the nonlinear resonant response, the linear natural frequencies are obtained via an eigenvalue analysis. Results are shown through frequency-response curves, force-response curves, time traces, phase-plane portraits, and fast Fourier transforms (FFTs). The effect of taking into account the length-scale parameter on the coupled nonlinear dynamic response of the system is also highlighted.

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Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory

Cited by 186 publications

References 35 publications

Size-dependent behavior of functionally graded sandwich microbeams based on the modified couple stress theory

Size-dependent behavior of functionally graded sandwich microbeams based on the modified couple stress theory

Thermal Effect on Free Vibration and Buckling of a Double-Microbeam System

Coupled Nonlinear Dynamics of Geometrically Imperfect Shear Deformable Extensible Microbeams

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