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Archive of Applied Mechanics

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19.11.2019 | Original

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

verfasst von: R. Barretta, S. Ali Faghidian, Francesco Marotti de Sciarra, M. S. Vaccaro

Erschienen in: Archive of Applied Mechanics | Ausgabe 4/2020

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Abstract

Nonlocal strain gradient continuum mechanics is a methodology widely employed in the literature to assess size effects in nano-structures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems. In the present study, it is proven that HOBC have to be replaced with univocally determined boundary conditions of constitutive type, established by a consistent variational formulation. The treatment, developed in the framework of torsion of elastic beams, provides an effective approach to evaluate scale phenomena in smaller and smaller devices of engineering interest. Both elastostatic torsional responses and torsional-free vibrations of nano-beams are investigated by applying a simple analytical method. It is also underlined that the nonlocal strain gradient model, if equipped with the inappropriate HOBC, can lead to torsional structural responses which unacceptably do not exhibit nonlocality. The presented variational strategy is instead able to characterize significantly peculiar softening and stiffening behaviors of structures involved in modern nano-electro-mechanical systems.

Vorheriger Artikel Exact closed-form static solutions for parabolic arches with concentrated damage

Nächster Artikel Suggestion of the DLV dimensionless number system to represent the scaled behavior of structures under impact loads

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Titel: Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions
verfasst von: R. Barretta
S. Ali Faghidian
Francesco Marotti de Sciarra
M. S. Vaccaro
Publikationsdatum: 19.11.2019
Verlag: Springer Berlin Heidelberg
Erschienen in: Archive of Applied Mechanics / Ausgabe 4/2020
Print ISSN: 0939-1533
Elektronische ISSN: 1432-0681
DOI: https://doi.org/10.1007/s00419-019-01634-w

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