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Engineering with Computers

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07.09.2020 | Original Article

Static bending of perforated nanobeams including surface energy and microstructure effects

verfasst von: Alaa A. Abdelrahman, Norhan A. Mohamed, Mohamed A. Eltaher

Erschienen in: Engineering with Computers | Sonderheft 1/2022

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Abstract

This article aims to present comprehensive model and analytical solution to investigate the static bending behavior of regularly squared cutout perforated thin/thick nanobeams incorporating the coupled effect of the microstructure and surface energy for the first time. The perforation influence is considered to be deriving equivalent geometrical and material characteristics. The modified couple stress theory is adopted to incorporate the microstructure effect while the modified Gurtin–Murdoch surface elasticity model is employed to incorporate the surface stress effect in perforated nanobeams. A variational formulation based on minimization of the total potential energy principle is employed to derive the equilibrium equations of perforated nanobeams based on both Euler–Bernoulli and Timoshenko beams theories are developed to investigate the associated effect of the shear deformation due to perforation process. Additionally, Poisson’s effect is also incorporated. Analytical closed-form for the non-classical bending profiles as well as the rotational displacement are developed for both beam theories considering the simultaneous effect of both couple stress and surface stress for both uniformly distributed and concentrated loading patterns. The verification of the developed model is verified and compared with previous works, and an excellent agreement is obtained. The applicability of the developed model is demonstrated and applied to study and analyze the nonclassical bending behavior of regularly squared perforated simply supported beams under different loading conditions. Additionally, effects of the perforation configuration parameters, beam size as well as beam aspect ratio on the bending behavior of perforated beams in the presence of microstructure and surface stress effects are also investigated and analyzed. The obtained results reveal that both couple stress and surface stress significantly affect the bending behavior of regularly squared cutout perforated beam structures. Results obtained are supportive for the design, analysis and manufacturing of perforated NEMS applications.

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Titel: Static bending of perforated nanobeams including surface energy and microstructure effects
verfasst von: Alaa A. Abdelrahman
Norhan A. Mohamed
Mohamed A. Eltaher
Publikationsdatum: 07.09.2020
Verlag: Springer London
Erschienen in: Engineering with Computers / Ausgabe Sonderheft 1/2022
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI: https://doi.org/10.1007/s00366-020-01149-x

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