A nonlinear strain gradient finite element for microbeams and microframes

Dadgar‐Rad, Farzam; Beheshti, Alireza

doi:10.1007/s00707-017-1798-3

Cited by 14 publications

(4 citation statements)

References 50 publications

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“…Some new terms in their study increased the stiffness of the microbeam in particular for the thin microbeam. Dadgar-Rad and Beheshti [306] proposed a nonlinear static bending behavior of microbeams as well as microframes with consideration of the strain gradient finite element method. They employed the Newton-Raphson method to investigate and solve the nonlinear governing relations.…”

Section: Nonlinear Static Bending Of Micro/nano-structuresmentioning

confidence: 99%

A review of size-dependent continuum mechanics models for micro- and nano-structures

Roudbari

Jorshari

et al. 2022

Thin-Walled Structures

101

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Section: Nonlinear Static Bending Of Micro/nano-structuresmentioning

confidence: 99%

A review of size-dependent continuum mechanics models for micro- and nano-structures

Roudbari

Jorshari

et al. 2022

Thin-Walled Structures

101

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“…The parametric study focused on the dependence of frequencies and critical loads upon the thickness-to-material length scale ratio. Additionally, Dadgar-Rad and Beheshti [15] explored the large deformation of microframes by a total Lagrange element, while Attia and Mohamed [16] considered thermal instability of FG microbeams using the DQM. Their finding reveals the importance of microstructural effect on the thermal stability and bending of the microbeams.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent nonlinear bending of microbeams based on a third-order shear deformation theory

Dang,

Nguyen,

2024

Vietnam J. Mech.

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In this paper, the size-dependent nonlinear bending of microbeams subjected to mechanical loading is studied using a finite element formulation. Based on the von Kármán nonlinear relationship and the third-order shear deformation theory, a size-dependent nonlinear beam element is derived by using the modified couple stress theory (MCST) to capture the microstructural size effect. The element with explicit expressions for the element vector of internal forces and tangent stiffness matrix is derived by employing the transverse shear rotation as a variable. Nonlinear bending of microbeams under different mechanical loading is predicted with the aid of Newton–Raphson iterative method. Numerical investigation shows that the derived element is efficient, and it is capable of giving accurate results by several elements. The obtained results reveal the importance of the micro-size effect on the nonlinear behavior of the microbeams, and the deflections are overestimated when the microstructural effect is ignored. The effects of the material length scale parameter, boundary conditions and loading type on the bending response of the microbeams are studied and highlighted.

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“…The results of the work reveal that the frequencies and critical buckling loads increase, but the nonlinear-to-linear frequency ratios as well as the deflections decrease by decreasing the thickness-to-material length scale ratio. A two-node total Lagrangian beam element using the fifth-order interpolation was Dadgar-Rad and Beheshti [22] for the geometrically nonlinear bending analysis of microbeams and microframes. The general form of Mindlin's strain gradient theory was used to capture the size effects at micron scales and Newton-Raphson method was adopted to compute the deformation of the microbeams and microframes.…”

Section: Introductionmentioning

confidence: 99%

Size dependent large displacements of microbeams and microframes

Nguyen²

2022

Vietnam J. Mech.

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The size dependent large displacement behavior of planar microbeams and microframes is studied in this paper using a corotational beam element. To account for the size effect, the modified couple stress theory (MCST) is employed in conjunction with Euler-Bernoulli beam theory in deriving the internal force vector and the tangent stiffness matrix of the beam element. The Newton-Raphson based iterative procedure is used in combination with the arc-length method to solve the nonlinear equilibrium equation and to trace the equilibrium paths. Various microbeams and microframes are analyzed to show the influence of the size effect on the large deflection behavior of the microstructure. The obtained result reveals that the size effect plays an important role on the large deflection response, and the displacements of the structure are over estimated by ignoring the size effect. A parametric study is carried out to highlight the influence of the material length scale parameter on the large displacement behavior of the microbeams and microframes.

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A nonlinear strain gradient finite element for microbeams and microframes

Cited by 14 publications

References 50 publications

A review of size-dependent continuum mechanics models for micro- and nano-structures

A review of size-dependent continuum mechanics models for micro- and nano-structures

Size-dependent nonlinear bending of microbeams based on a third-order shear deformation theory

Size dependent large displacements of microbeams and microframes

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