Analysis of large deflection of nanobeams based on the modified couple stress theory by using finite element method

Estabragh, Ehsan Raeisi; Baradaran, Gholam Hossein

doi:10.1007/s00419-021-02029-6

Cited by 10 publications

(5 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Abouelregal and Marin [12] used the MCST to develop the Euler-Bernoulli beam model for the investigation of the temperature-dependent properties within the nanobeam. All those research works [9][10][11][12] confirmed the capability of the MCST to represent the small-scale effect in the nanostructures.…”

Section: Introductionmentioning

confidence: 64%

“…The MCST is one of these theories that has become popular in the last two decades to address the small-scale effect inherent in micro-and nanoscale structures. For example, Espo et al [9] developed the piezoelectric phononic crystal nanobeam based on the MCST for the flexure wave band structure analysis, while Estabragh and Baradaran [10] developed the finite beam model based on the MCST to investigate the large deflection of the nanobeam. Jazi [11] employed the MCST to enhance the Timoshenko beam for the nonlinear force vibration analysis of an elastically connected double nanobeam system.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Size-Scale Effects on Bending Behaviour of Nanobeam on an Elastic Substrate Medium

Limkatanyu

2023

GEOMATE

View full text Add to dashboard Cite

This paper presents a new nonlocal beam-substrate medium model for the static bending analysis of micro-and nano-sized Euler-Bernoulli beam systems resting on an elastic substrate medium. The modified couple stress theory (MCST) represents the small-scale effect (nonlocal effect) inherent in microand nanoscale structures. The Winkler-Pasternak foundation model is used to model the characteristics of the underlying substrate medium, while the surface continuum model of Gurtin and Murdoch is employed to account for the size-dependent effect (surface-energy effect). The governing differential equation and its associated boundary conditions for the proposed beam-substrate medium model are derived based on the principle of virtual displacement. These equations are employed to assess the bending behavior of the nanobeam system on the elastic substrate medium. The analytical results are discussed through a numerical simulation, and this reveals that the small-scale effect, as well as size-dependent and substrate-structure interaction effects, lead to stiffness enhancement in the system.

show abstract

Section: Introductionmentioning

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Size-Scale Effects on Bending Behaviour of Nanobeam on an Elastic Substrate Medium

Limkatanyu

2023

GEOMATE

View full text Add to dashboard Cite

show abstract

“…In some experimental and theoretical research , it is shown that classical elastic theories cause many errors when they have been employed for nanosized structures. To tackle this situation, different higher-order elasticity theories such as doublet mechanics Mohamed 2020, Civalek et al 2021), couple stress (Fan et al 2020), strain gradient elasticity (Akgöz and Civalek 2011, Ansari et al 2016, Yin et al2022, Jiang et al 2022, Bagheri et al 2021, nonlocal strain gradient elasticity (Lim et al 2015, Zhou et al 2023, Xu et al 2022, Boyina et al 2022, Anh et al 2022, Norouzzadeh et al 2019, nonlocal elasticity (NE) (Vosoughi 2016, Vosoughi et al 2018, Eringen and Suhubi 1964, Eringen 1983, Eltaher et al 2023, Mohammed et al 2022, Kumar et al 2021, and modified couple stress theory (Mohtashami and Beni 2019, Asghari et al 2011, Kahrobaiyan et al 2014, Liu and Peng 2022, Zhao and He 2023, Raeisi Estabragh and Baradaran 2021, surface energy (Eltaher et al 2019, Xu andFan 2016), peridynamic model (Yang et al 2022) have been used to overcome small-size effects. Barati (2018) has studied the dynamic analysis of FG porous nanoshells with uneven and even distributions.…”

Section: Introductionmentioning

confidence: 99%

A combined method for the stability characteristics of FG a nanobeam embedded in an elastic matrix

Uzun,

Yaylı

2024

Preprint

View full text Add to dashboard Cite

The investigation conducted in this work aims to investigate the stability response of functionally graded restrained nanobeams with four different porosity distributions and embedded in the Winkler foundation. To take into concern the size effects, Eringen's nonlocal elasticity is employed as a higher-order continuum theory. The material properties of the functionally graded porous nano-sized beam with deformable boundaries are changed gradually in spatial coordinates through the power-law model which covers four kinds of porosity distributions. A system of linear equations consists of infinite power series for an embedded functionally graded porous nanobeam under axial point loads obtained from Fourier trigonometric series and Stokes’ transformation is solved by an eigenvalue problem which satisfies rigid or deformable supporting conditions including classical boundary conditions such as simply supported, clamped-clamped and clamped-pinned. Analytical results are obtained for various porosity distributions and boundary conditions to reveal the effects of nonlocality, Winkler foundation and power-law index on the lateral buckling behavior of a functionally graded nanoscale nanobeam.

show abstract

“…Typically, the first step involves the proposal of a mathematical framework that is appropriate to describe the mechanical behavior of these systems. By contrasting the findings of the theoretical framework with experimental data, it is then possible to determine the mechanical properties of the nanostructures [2].…”

Section: Introductionmentioning

confidence: 99%

A modified couple stress model to analyze the effect of size-dependent on thermal interactions in rotating nanobeams whose properties change with temperature

Abouelregal,

Rabih,

Alharbi

et al. 2024

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

Understanding the behavior of rotating materials and structures on small scales is crucial for many scientific and engineering fields, and such studies play an important role in this regard. This paper aims to propose a novel paradigm for analyzing the vibrational characteristics of thermoelastic nanobeams with diverse physical attributes. The incorporation of size effects in the structural and thermal constitutive relationships involves the consideration of nonlocal elasticity theory (NET) and the modified couple stress (MCS) model, together with the utilization of the Euler–Bernoulli assumptions for thin beams. The work also involves the development of a new non-Fourier thermoelasticity model that incorporates the Moore–Gibson–Thompson (MGT) equation. Furthermore, it was taken into account that the thermal conductivity of the flexible materials is not consistent but rather changes with temperature. Periodic pulse heating was applied to rotating nanobeams, and the behavior of the nanobeams was investigated with respect to thermal, rotational, and length-scale effects. To demonstrate the impact of the distinctive characteristics of the MCS and MGT thermoelastic models on the physical fields, a range of numerical data are presented. The study also investigated the propagation characteristics of thermo-mechanical waves, taking into account aspects such as thermal relaxation time and the influence of temperature change on physical properties. Based on the observed results, including the size impact in the structural and thermal equations can lead to significant disparities when compared to conventional models. The inclusion of the length-scale component in the MCS theory, which increases the rigidity and hardiness of the nanobeam structure, may help to explain the observed effect.

show abstract

Analysis of large deflection of nanobeams based on the modified couple stress theory by using finite element method

Cited by 10 publications

References 35 publications

Size-Scale Effects on Bending Behaviour of Nanobeam on an Elastic Substrate Medium

Size-Scale Effects on Bending Behaviour of Nanobeam on an Elastic Substrate Medium

A combined method for the stability characteristics of FG a nanobeam embedded in an elastic matrix

A modified couple stress model to analyze the effect of size-dependent on thermal interactions in rotating nanobeams whose properties change with temperature

Contact Info

Product

Resources

About