Static and dynamic analysis of the postbuckling of bi-directional functionally graded material microbeams

Chen, Xiaochao; Zhang, Xuanling; Lü, Yixin; Li, Yinghui

doi:10.1016/j.ijmecsci.2018.12.001

Cited by 72 publications

(19 citation statements)

References 70 publications

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“…The postbuckling loads obtained in Eqs. (22), (24), (25) and (26) can lead to the critical buckling loads N cr when the postbuckling amplitude is set to zero W = 0.…”

Section: Solutionmentioning

confidence: 99%

“…In the literature, a wide range of studies have been done on the vibration, buckling and postbuckling analyses of beams especially micro-or nano-beams [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33], but there are few studies on the postbuckling analysis of porous micro-or nanostructures [34][35][36][37]. She et al [34] presented the thermal buckling and postbuckling of FG nanotubes with porosities.…”

Section: Introductionmentioning

confidence: 99%

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Effect of nano-porosity on postbuckling of non-uniform microbeams

Khorshidi

2019

SN Appl. Sci.

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This study is accomplished to investigate the effect of different types of porosity distribution on the static postbuckling response of non-uniform microbeams under the simply supported boundary conditions. The modified couple stress theory is used to capture the size effect in microscales, and the von-Karman strain-displacement relation is employed to describe the nonlinearity effect. The relative elasticity characteristics, e.g., Young's modulus and the material length scale parameter, are considered as a function of relative mass density. The nonlinear governing equations for Euler-Bernoulli porous microbeams with non-uniform cross section are derived by a variational energy method and solved using a closed-form solution. The critical buckling load and the static postbuckling response of porous non-uniform microbeams, non-porous non-uniform microbeams and porous uniform microbeams are compared with together. Therefore, effects of nano-porosity and non-uniformity on the postbuckling behavior of the microbeam are investigated.

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“…The postbuckling loads obtained in Eqs. (22), (24), (25) and (26) can lead to the critical buckling loads N cr when the postbuckling amplitude is set to zero W = 0.…”

Section: Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of nano-porosity on postbuckling of non-uniform microbeams

Khorshidi

2019

SN Appl. Sci.

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“…For example, Chen et al [25] analyzed the linear buckling, vibration, and stability behaviors of BDFG microbeams embedded in elastic medium using the modified couple stress theory. Considering the von Karman nonlinear strain, Chen et al [26] investigated the nonlinear large deflection of BDFG microbam in the postbuckling domain, and the mode veering phenomenon is explored in the postbuckling vibration. Based on the modified couple stress theory accompanying with transverse shear-normal deformation beam theory, Karamanli and Aydogdu [27] investigated the free oscillation of the rotating BDFG porous sandwich microbeams and found that the lightweight and low-cost objectives can be achieved by controlling the material and porosity distribution through the structure.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Parametric Dynamics of Bidirectional Functionally Graded Beams

Lü¹,

Chen

2020

Shock and Vibration

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“…In the case of functionally graded (FG) micro-and nanobeams, many papers are published to explore their vibration characteristics. [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] It was concluded that the microstructure e®ect via the MCST increases the sti®ness-hardening of FG micro-and nanoscale beams.…”

Section: Introductionmentioning

confidence: 99%

Surface Energy Effects on the Nonlinear Free Vibration of Functionally Graded Timoshenko Nanobeams Based on Modified Couple Stress Theory

Attia

Shanab

Mohamed

et al. 2019

Int. J. Str. Stab. Dyn.

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An integrated nonlinear couple stress-surface energy continuum model is developed to study the nonlinear vibration characteristics of size-dependent functionally graded nanobeams for the first time. The nanobeam theory is formulated based on the Timoshenko kinematics, augmented by von Kármán’s geometric nonlinearity. The modified couple stress and Gurtin–Murdoch surface elasticity theories are incorporated to capture the long-range interaction and surface energy, respectively. Unlike existing Timoshenko nanobeam models, the effects of surface elasticity, residual surface stress, surface mass density and Poisson’s ratio, in addition to bending and axial deformations, are incorporated in the newly developed model. A power law function is used to model the material distribution through the thickness of the beam, considering the gradation of bulk and surface material parameters. A variational formulation of the nonlinear nonclassical governing equations and associated nonclassical boundary conditions is established by employing Hamilton’s principle. The generalized differential quadrature method is exploited in conjunction with either the Pseudo-arclength continuation or Runge–Kutta method to solve the problem with an exact implementation of the nonclassical boundary conditions. The formulation and solution procedure presented are verified by comparing the obtained results with available ones. Based on the parametric study, it is concluded that the nonclassical boundary conditions, material length scale parameter, residual surface stress, surface elasticity, bulk elasticity modulus, gradient index, nonlinear amplitude and thickness have important influences on the linear and nonlinear vibration responses of functionally graded Timoshenko nanobeams.

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Static and dynamic analysis of the postbuckling of bi-directional functionally graded material microbeams

Cited by 72 publications

References 70 publications

Effect of nano-porosity on postbuckling of non-uniform microbeams

Effect of nano-porosity on postbuckling of non-uniform microbeams

Nonlinear Parametric Dynamics of Bidirectional Functionally Graded Beams

Surface Energy Effects on the Nonlinear Free Vibration of Functionally Graded Timoshenko Nanobeams Based on Modified Couple Stress Theory

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