The influence of size-dependent shear deformation on mechanical behavior of microstructures-dependent beam based on modified couple stress theory

Dehrouyeh-Semnani, Amir Mehdi; Nikkhah‐Bahrami, Mansour

doi:10.1016/j.compstruct.2014.12.038

Cited by 44 publications

(11 citation statements)

References 77 publications

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“…Unlike the von Karman nonlinear theory, the modified von Karman nonlinear theory did include the nonlinear terms due to the transverse normal strain, and thus requiring 2D constitutive relations of beams. The EBT and TBT elements developed by Arbind and Reddy [391] were employed by Dehrouyeh-Semnani and Nikkhah-Bahrami [394] to examine the size effect on the bending, buckling and free vibration responses of isotropic microbeams. Kahrobaiyan et al [395] also developed a two-node modified couple stress TBT element for the static bending analysis of isotropic microbeams.…”

Section: Modified Couple Stress Elementsmentioning

confidence: 99%

A review of continuum mechanics models for size-dependent analysis of beams and plates

Thai

Nguyen

et al. 2017

Composite Structures

304

109

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This paper presents a comprehensive review on the development of higher-order continuum models for capturing size effects in small-scale structures. The review mainly focus on the size-dependent beam, plate and shell models developed based on the nonlocal elasticity theory, modified couple stress theory and strain gradient theory due to their common use in predicting the global behaviour of small-scale structures. In each higher-order continuum theory, various size-dependent models based on the classical theory, first-order shear deformation theory and higher-order shear deformation theory were reviewed and discussed. In addition, the development of finite element solutions for size-dependent analysis of beams and plates was also highlighted. Finally a summary and recommendations for future research are presented. It is hoped that this review paper will provide current knowledge on the development of higher-order continuum models and inspire further applications of these models in predicting the behaviour of micro-and nano-structures.

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Section: Modified Couple Stress Elementsmentioning

confidence: 99%

A review of continuum mechanics models for size-dependent analysis of beams and plates

Thai

Nguyen

et al. 2017

Composite Structures

304

109

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“…in a longitudinal magnetic field by Wang, Liu, and Dai (2015), the influence of size-dependent shear deformation on mechanical behavior of micro-structures-dependent beam using finite element method by Dehrouyeh-Semnani and Nikkhah-Bahrami (2015c), and internal energy transfer in dynamical behaviour of Timoshenko microarches by Ghayesh and Farokhi (2015a).…”

Section: Introductionmentioning

confidence: 99%

A damped sandwich beam model based on symmetric–deviatoric couple stress theory

Dehrouyeh-Semnani

Dehrouyeh

Torabi-Kafshgari

et al. 2015

International Journal of Engineering Science

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“…23 developed a two-node finite element for microbeams based on Timoshenko beam theory (TBT). Dehrouyeh-Semnani and Nikkhah-Bahrami 24 studied the effect of size-dependent shear deformation on static, buckling, and free vibration behavior of microbeams. Considering EBT, Bambill et al.…”

Section: Introductionmentioning

confidence: 99%

“…Considering the equilibrium of moments of couples, MCST is developed by Yang et al 3 based on classical couple stress theory [15][16][17][18] that originally required two material length scale parameters. Research reports on static and dynamic analyses of homogeneous microbeams based on MCST are available in the literature and some of them 4,[19][20][21][22][23][24][25][26] are briefly mentioned here. The static and free vibration analysis of Euler-Bernoulli microbeams based on variational approach is reported by Park and Gao 4 and Kong et al 19 respectively.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear forced vibration analysis of higher order shear-deformable functionally graded microbeam resting on nonlinear elastic foundation based on modified couple stress theory

Das

2018

Proceedings of the IMechE

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Geometrically nonlinear forced vibration analysis of higher order shear-deformable functionally graded microbeam is presented, where the beam is supported on a three-parameter Winkler–Pasternak-type nonlinear elastic foundation and subjected to a harmonically varying distributed load. The modified couple stress theory of elasticity is employed in the formulation to address the size-dependent effect. Hamilton’s principle is used to derive the displacement-based governing equations considering Reddy’s third-order shear deformation theory. Ritz method is followed to convert the governing equations to nonlinear algebraic form in the frequency domain by approximating the displacement fields. A mixed algorithm for nonlinear equations based on the iterative substitution method with successive relaxation and Broyden’s method is successfully employed to solve the stable regions of the frequency-response curves. The results are presented for hinged and clamped beams, and the effects of different parameters such as size-dependent thickness, load amplitude, foundation parameters, and gradation-profile parameter are studied. The effect of thermal loading due to uniform temperature rise is also studied considering temperature-dependent material properties.

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The influence of size-dependent shear deformation on mechanical behavior of microstructures-dependent beam based on modified couple stress theory

Cited by 44 publications

References 77 publications

A review of continuum mechanics models for size-dependent analysis of beams and plates

A review of continuum mechanics models for size-dependent analysis of beams and plates

A damped sandwich beam model based on symmetric–deviatoric couple stress theory

Nonlinear forced vibration analysis of higher order shear-deformable functionally graded microbeam resting on nonlinear elastic foundation based on modified couple stress theory

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