A non-classical Kirchhoff rod model based on the modified couple stress theory

Zhang, Gongye

doi:10.1007/s00707-018-2279-z

Cited by 20 publications

(10 citation statements)

References 47 publications

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“…Various non-classical models of micro-and nano-rod have been provided for example in refs. [20][21][22]. Surface elasticity has been used in the bending of nano-wires in refs.…”

Section: Introductionmentioning

confidence: 99%

Buckling of a nano‐rod with taken into account of surface effect

Bochkarev

2023

Z Angew Math Mech

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Buckling of a simple supported and cantilever nano‐rod and under action of self‐weight was modeled, taking into account the surface effect according to two models of surface elasticity – Gurtin–Murdoch and Steigmann–Ogden. The size effect under the buckling was studied by the Ritz method using two kinematic hypotheses, known as the rod theories of Euler–Bernoulli and Timoshenko. The simulation results were compared depending on the accepted surface elasticity model and the kinematic hypothesis.

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“…Various non-classical models of micro-and nano-rod have been provided for example in refs. [20][21][22]. Surface elasticity has been used in the bending of nano-wires in refs.…”

Section: Introductionmentioning

confidence: 99%

Buckling of a nano‐rod with taken into account of surface effect

Bochkarev

2023

Z Angew Math Mech

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“…Several works have also used couple-stress theories to account for size effects in Kirchhoff rods. [ZG19] For ease of notation, we only consider ε k := 1/k in the following, but it would also be possible to work with arbitrary interatomic distances, see [BS22].…”

Section: Introductionmentioning

confidence: 99%

A bending-torsion theory for thin and ultrathin rods as a $Γ$-limit of atomistic models

Schmidt¹,

Zeman²

2022

Preprint

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The purpose of this note is to establish two continuum theories for the bending and torsion of inextensible rods as Γ-limits of 3D atomistic models. In our derivation we study simultaneous limits of vanishing rod thickness h and interatomic distance ε. First, we set up a novel theory for ultrathin rods composed of finitely many atomic fibres (ε ∼ h), which incorporates surface energy and new discrete terms in the limiting functional. This can be thought of as a contribution to the mechanical modelling of nanowires. Second, we treat the case where ε h and recover a nonlinear rod model -the modern version of Kirchhoff's rod theory.

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“…The bandgap for elastic wave propagation arises from the Bragg scattering and local resonance [11][12][13]. As a result, thin structures (e.g., rods, beams, plates and shells) usually exhibit size-dependent effects at small scales [14][15][16][17][18][19][20][21][22][23][24][25], which cannot be captured by the existing classical theories. The same phenomenon also happens in bandgaps made of micro-/nano-PC structures.…”

Section: Introductionmentioning

confidence: 99%

Tunable Bandgaps in Phononic Crystal Microbeams Based on Microstructure, Piezo and Temperature Effects

Hong

Zhang

et al. 2021

Crystals

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A new model of non-classical phononic crystal (PC) microbeam for the elastic wave bandgap generation is provided, incorporating microstructure, piezomagnetism, piezoelectricity and temperature effects. The wave equation of a general magneto–electro–elastic (MEE) phononic crystal microbeam is derived, which recovers piezoelectric- and piezomagnetic-based counterparts as special cases. The piezomagnetic and piezoelectric materials are periodically combined to construct the PC microbeam and corresponding bandgaps are obtained by using the plane wave expansion (PWE) method. The effects of the piezomagnetism, piezoelectricity, microstructure, geometrical parameters and applied multi-fields (e.g., external electric potential, external magnetic potential, temperature change) on the bandgaps are discussed. The numerical results reveal that the bandgap frequency is raised with the presence of piezo and microstructure effects. In addition, the geometry parameters play an important role on the bandgap. Furthermore, large bandgaps can be realized by adjusting the external electric and magnetic potentials at micron scale, and lower bandgap frequency can be realized through the temperature rise at all length scales.

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A non-classical Kirchhoff rod model based on the modified couple stress theory

Cited by 20 publications

References 47 publications

Buckling of a nano‐rod with taken into account of surface effect

Buckling of a nano‐rod with taken into account of surface effect

A bending-torsion theory for thin and ultrathin rods as a $Γ$-limit of atomistic models

Tunable Bandgaps in Phononic Crystal Microbeams Based on Microstructure, Piezo and Temperature Effects

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