The size-dependent analysis of microplates via a newly developed shear deformation theory

Bahreman, M.; Darijani, H.; Fard, A. Bahrani

doi:10.1007/s00707-018-2260-x

Cited by 11 publications

(5 citation statements)

References 40 publications

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“…Furthermore, considering the stiffness of the microplate (by a dimensionless parameter b), N xx ¼ N yy ¼ N becomes (Bahreman et al, 2019;Das and Bhushan, 2023;Mukherjee et al, 2005):…”

Section: Galerkin-fem Approachmentioning

confidence: 99%

“…< 1 is a dimensionless positive parameter that considers, through C f , the possible nonuniform distribution of the electric charge on d-microplate (Dastidar et al, 2023;Kumar et al, 2021). In ( 17), the dependence on V of the action control determines the E in the device, which, in turn, generates an electrostatic pressure that moves the deformable plate (Di Bahreman et al, 2019;Das and Bhushan, 2023). Remark 4 Equation ( 18) does not consider contributions due to any local mechanical stresses, which would reduce the deflection by a few percentage points.…”

Section: The Micro-electron-mechanical-systems Capacitive Control Cir...mentioning

confidence: 99%

“…, 2021 ). In (17), the dependence on V of the action control determines the E in the device, which, in turn, generates an electrostatic pressure that moves the deformable plate ( Di Barba et al ., 2022 ; Bahreman et al ., 2019 ; Das and Bhushan, 2023 ) .…”

Section: The Dynamic Continuous Modelmentioning

confidence: 99%

“…Neglecting the effects of stiffness compared to those of stretching [a hypothesis valid in the conditions of small deflections (Bahreman et al. , 2019)], we obtain a more numerically solvable version of model: …”

Section: Numerical Recovering Of the D-microplatementioning

confidence: 99%

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Galerkin-FEM approach for dynamic recovering of the plate profile in electrostatic MEMS with fringing field

Versaci,

Angiulli,

Fattorusso

et al. 2024

COMPEL

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Purpose Based on previous results of the existence, uniqueness, and regularity conditions for a continuous dynamic model for a parallel-plate electrostatic micro-electron-mechanical-systems with the fringing field, the purpose of this paper concerns a Galerkin-FEM procedure for deformable element deflection recovery. The deflection profiles are reconstructed by assigning the dielectric properties of the moving element. Furthermore, the device’s use conditions and the deformable element’s mechanical stresses are presented and discussed. Design/methodology/approach The Galerkin-FEM approach is based on weighted residuals, where the integrals appearing in the solution equation have been solved using the Crank–Nicolson algorithm. Findings Based on the connection between the fringing field and the electrostatic force, the proposed approach reconstructs the deflection of the deformable element, satisfying the conditions of existence, uniqueness and regularity. The influence of the electromechanical properties of the deformable plate on the method has also been considered and evaluated. Research limitations/implications The developed analytical model focused on a rectangular geometry. Practical implications The device studied is suitable for industrial and biomedical applications. Originality/value This paper proposed numerical approach characterized by low CPU time enables the creation of virtual prototypes that can be analyzed with significant cost reduction and increased productivity.

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“…Furthermore, considering the stiffness of the microplate (by a dimensionless parameter b), N xx ¼ N yy ¼ N becomes (Bahreman et al, 2019;Das and Bhushan, 2023;Mukherjee et al, 2005):…”

Section: Galerkin-fem Approachmentioning

confidence: 99%

Section: The Micro-electron-mechanical-systems Capacitive Control Cir...mentioning

confidence: 99%

Section: The Dynamic Continuous Modelmentioning

confidence: 99%

Section: Numerical Recovering Of the D-microplatementioning

confidence: 99%

See 2 more Smart Citations

Galerkin-FEM approach for dynamic recovering of the plate profile in electrostatic MEMS with fringing field

Versaci,

Angiulli,

Fattorusso

et al. 2024

COMPEL

View full text Add to dashboard Cite

show abstract

“…Tho et al [23] employed the finite element method (FEM) and an unique third-order shear deformation beam theory (TSDT) to predict the static bending and free vibration responses of rotating (around a fixed axis) piezoelectric nanobeams with geometrical imperfection and flexoelectric effects. Other publications [24][25][26][27] include some excellent work on mechanical responses of microstructures.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear static bending analysis of microplates resting on imperfect two-parameter elastic foundations using modified couple stress theory

Dung¹,

Thai²,

Tran³

et al. 2022

Comptes Rendus. Mécanique

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The nonlinear static bending analysis of microplates resting on imperfect Pasternak elastic foundations is carried out in this paper. The finite element method based on the modified couple stress theory is used to derive the nonlinear finite element formulations. The present theory and mathematical model are validated by comparisons of this work's results with those of other reputable publications, which show a very good agreement. The influences of length-scale parameter, nonlinearity, elastic foundation parameters, imperfect foundations, and boundary conditions on the nonlinear static bending response of microplates are then explored. The computed data of this study is very intriguing, particularly the interaction of the microplate with the imperfect elastic foundation, and this helps us better understand the mechanical behavior of this structure.

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Instability analysis of moderately thick porous micro-plate via two-variable strain gradient theory

Farahmand

yasaie

2021

Arch Appl Mech

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The size-dependent analysis of microplates via a newly developed shear deformation theory

Cited by 11 publications

References 40 publications

Galerkin-FEM approach for dynamic recovering of the plate profile in electrostatic MEMS with fringing field

Galerkin-FEM approach for dynamic recovering of the plate profile in electrostatic MEMS with fringing field

Nonlinear static bending analysis of microplates resting on imperfect two-parameter elastic foundations using modified couple stress theory

Instability analysis of moderately thick porous micro-plate via two-variable strain gradient theory

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