Static analysis of planar arbitrarily curved microbeams with the modified couple stress theory and Euler-Bernoulli beam model

Vo, Duy; Suttakul, Pana; Rungamornrat, Jaroon; Nanakorn, Pruettha

doi:10.1016/j.apm.2022.08.005

Cited by 14 publications

(1 citation statement)

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“…Based on Mindlin's strain gradient theory, a linear model of Bernoulli-Euler beams has been presented by Niiranen et al [24], and a geometrically non-linear model was further developed by Tran and Niiranen [25] by adopting the von Kármán strain assumption. Based on the modified couple stress theory, Vo et al presented the models of planar [26] and spatial [27] arbitrarily curved micro-beams and Li et al investigated the bending and free vibration of bi-directional functionally graded graphene nano-platelets-reinforced composite microbeams [28]. However, these existing models are contradictory [29].…”

Section: Introductionmentioning

confidence: 99%

On Strain Gradient Theory and Its Application in Bending of Beam

Wang

Song

et al. 2022

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The general strain gradient theory of Mindlin is re-visited on the basis of a new set of higher-order metrics, which includes dilatation gradient, deviatoric stretch gradient, symmetric rotation gradient and curvature. A strain gradient bending theory for plane-strain beams is proposed based on the present strain gradient theory. The stress resultants are re-defined and the corresponding equilibrium equations and boundary conditions are derived for beams. The semi-inverse solution for a pure bending beam is obtained and the influence of the Poisson’s effect and strain gradient components on bending rigidity is investigated. As a contrast, the solution of the Bernoulli–Euler beam is also presented. The results demonstrate that when Poisson’s effect is ignored, the result of the plane-strain beam is consistent with that of the Bernoulli–Euler beam in the couple stress theory. While for the strain gradient theory, the bending rigidity of a plane-strain beam ignoring the Poisson’s effect is smaller than that of the Bernoulli–Euler beam due to the influence of the dilatation gradient and the deviatoric stretch gradient along the thickness direction of the beam. In addition, the influence of a strain gradient along the length direction on a bending rigidity is negligible.

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