An efficient 3-node triangular plate element for static and dynamic analyses of microplates based on modified couple stress theory with micro-inertia

Mao, Yu-Hao; Shang, Yan; Cen, Song; Li, Chenfeng

doi:10.1007/s00366-022-01715-5

Cited by 3 publications

(1 citation statement)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These micro/nanostructures, e.g. graphene and carbon nanotubes, can be reduced to one-or two-dimensional structures like beams, plates, and membranes [1][2][3][4][5][6][7][8][9]. Microscopic phenomena such as surface effects, size effects and quantum effects play an important role in these micro/nanostructures [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

A novel hybrid 8-node plate element for capturing the nonlocal effect based on the Hellinger-Reissner variational principle

Li,

Yao,

et al. 2024

Preprint

View full text Add to dashboard Cite

The Hellinger-Reissner variational principle based hybrid finite element method (FEM) is developed and applied to study the nonlocal mechanics of plates and beams at a micro/nano-scale. For this purpose, a plane 8-node plate element termed as MHAS-24β with 24 independent internal force parameters is proposed to modelling the mechanical behaviors including static bending, free vibration and buckling. The Mindlin plate theory allows the use of generalized displacement to satisfy \({\text{C}}^{\text{0}}\) continuity requirements, making it applicable to plates with different thicknesses. To overcome shear locking, the assumed strain method (ASM) is adopted to modify original strains. The polynomials for internal forces are assumed to be related to the highest-order derivatives of variables, making them complete and capable of avoiding the zero-energy mode. The posterior error estimation indicates that the convergence order is not affected by the nonlocal parameter, plate thickness or element shape. The MHAS-24β element effectively captures the nonlocal effect and outperforms the displacement-type FEM and the low-order hybrid FEM described in previous literature.

show abstract

Section: Introductionmentioning

confidence: 99%

A novel hybrid 8-node plate element for capturing the nonlocal effect based on the Hellinger-Reissner variational principle

Li,

Yao,

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

Isogeometric analysis of shear-deformable, in-plane functionally graded microshells by Mindlin’s strain gradient theory

Aung

et al. 2023

Engineering with Computers

View full text Add to dashboard Cite

Size-dependent buckling and instability of a porous microplate under electrostatic fields and Casimir forces

Mojahedi,

Ayatollahi

2024

Arch Appl Mech

View full text Add to dashboard Cite

An efficient 3-node triangular plate element for static and dynamic analyses of microplates based on modified couple stress theory with micro-inertia

Cited by 3 publications

References 52 publications

A novel hybrid 8-node plate element for capturing the nonlocal effect based on the Hellinger-Reissner variational principle

A novel hybrid 8-node plate element for capturing the nonlocal effect based on the Hellinger-Reissner variational principle

Isogeometric analysis of shear-deformable, in-plane functionally graded microshells by Mindlin’s strain gradient theory

Size-dependent buckling and instability of a porous microplate under electrostatic fields and Casimir forces

Contact Info

Product

Resources

About