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Nonlocal Gradient Mechanics of Elastic Beams Under Torsion

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Size-Dependent Continuum Mechanics Approaches

Part of the book series: Springer Tracts in Mechanical Engineering ((STME))

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Abstract

Nonlocal gradient mechanics of elastic beams subject to torsion is established by means of a variationally consistent methodology, equipped with suitable functional spaces of test fields. The proposed elasticity theory is the generalization of size-dependent models recently contributed in literature to assess size-effects in nano-structures, such as modified nonlocal strain gradient and strain- and stress-driven local/nonlocal elasticity formulations. General new ideas are elucidated by examining the torsional behavior of elastic nano-beams. Equivalence between nonlocal integral convolutions and differential problems subject to variationally consistent boundary conditions is demonstrated for special averaging kernels. The variational procedure leads to well-posed engineering problems in nano-mechanics. Elasto-static responses and free vibrations of nano-beams under torsion are analyzed applying an effective analytical solution technique. Nonlocal strain- and stress-driven gradient models of elasticity can efficiently predict both stiffening and softening structural responses, and thus, notably characterize small-scale phenomena in structures exploited in modern Nano-Electro-Mechanical-Systems (NEMS).

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Acknowledgements

The financial support of the Italian Ministry for University and Research (P.R.I.N. National Grant 2017, Project code 2017J4EAYB; “University of Naples Federico II” Research Unit) is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Structures for Engineering and Architecture, University of Naples Federico II, Via Claudio 21, 80125, Naples, Italy

    Francesco P. Pinnola, Marzia S. Vaccaro, Raffaele Barretta & Francesco Marotti de Sciarra

  2. Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    S. Ali Faghidian

Authors
  1. Francesco P. Pinnola
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  2. S. Ali Faghidian
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  3. Marzia S. Vaccaro
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  4. Raffaele Barretta
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  5. Francesco Marotti de Sciarra
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Corresponding author

Correspondence to Raffaele Barretta .

Editor information

Editors and Affiliations

  1. School of Mechanical Engineering, Shiraz University, Shiraz, Iran

    Esmaeal Ghavanloo

  2. School of Mechanical Engineering, Shiraz University, Shiraz, Iran

    S. Ahmad Fazelzadeh

  3. Department of Structures for Engineering and Architecture, University of Naples Federico II, Naples, Italy

    Francesco Marotti de Sciarra

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Pinnola, F.P., Faghidian, S.A., Vaccaro, M.S., Barretta, R., Marotti de Sciarra, F. (2021). Nonlocal Gradient Mechanics of Elastic Beams Under Torsion. In: Ghavanloo, E., Fazelzadeh, S.A., Marotti de Sciarra, F. (eds) Size-Dependent Continuum Mechanics Approaches. Springer Tracts in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-63050-8_7

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  • DOI: https://doi.org/10.1007/978-3-030-63050-8_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-63049-2

  • Online ISBN: 978-3-030-63050-8

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