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International Journal for Multiscale Computational Engineering

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ISSN Imprimir: 1543-1649

ISSN On-line: 1940-4352

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ON NONLOCAL LAM STRAIN GRADIENT MECHANICS OF ELASTIC RODS

Volume 18, Edição 1, 2020, pp. 67-81
DOI: 10.1615/IntJMultCompEng.2019030655
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Raffaele Barretta
Department of Structures for Engineering and Architecture, University of Naples Federico II, via Claudio 21, 80125 Naples, Italy
S. Ali Faghidian
Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
F. Marotti de Sciarra
Department of Structures for Engineering and Architecture, University of Naples Federico II, via Claudio 21, 80125 Naples, Italy
F. P. Pinnola
Department of Structures for Engineering and Architecture, University of Naples Federico II, via Claudio 21, 80125 Naples, Italy

RESUMO

Numerous contributions can be found in the recent literature exploiting the nonlocal strain gradient model, introduced in consequence of unification of the differential relation (consequent but not equivalent to Eringen nonlocal integral law) and strain gradient elasticity. In the present paper, Eringen nonlocal integral and Lam modified strain gradient theories are coupled to formulate a nonlocal Lam strain gradient model of elasticity. Three scale parameters, describing nonlocality, dilatation, and stretch gradient, are utilized to significantly estimate size-dependent responses of 1D nanocontinua. The governing constitutive law is established via a variationally consistent approach, based on suitably selected test fields, projected for formulating well-posed static and dynamic problems of engineering interest. The nonlocal Lam strain gradient model, developed for nanorods, provides axial force fields in terms of integral convolutions involving elastic axial strain fields. The integral law, equivalent to an expedient set of constitutive differential and boundary conditions, is exploited for studying static and free vibration behaviors of simple nanostructural schemes. Exact analytical solutions are gotten in terms of nonlocal and gradient characteristic parameters. Validation of the proposed strategy is carried out by comparing the contributed results with those obtained by the modified nonlocal strain gradient theory.

Palavras-chave: nanocontinua, Lam strain gradient elasticity, nonlocal integral elasticity, modified nonlocal strain gradient elasticity, size effects, analytical modeling, NEMS
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CITADO POR

  1. Faghidian S. Ali, Higher–order nonlocal gradient elasticity: A consistent variational theory, International Journal of Engineering Science, 154, 2020. Crossref

  2. Faghidian S. Ali, Ghavanloo Esmaeal, Unified higher-order theory of two-phase nonlocal gradient elasticity, Meccanica, 56, 3, 2021. Crossref

  3. Pisano Aurora Angela, Fuschi Paolo, Polizzotto Castrenze, Integral and differential approaches to Eringen's nonlocal elasticity models accounting for boundary effects with applications to beams in bending, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 101, 8, 2021. Crossref

  4. Fazlali Mahdad, Faghidian S. Ali, Asghari Mohsen, Shodja Hossein M., Nonlinear flexure of Timoshenko–Ehrenfest nano-beams via nonlocal integral elasticity, The European Physical Journal Plus, 135, 8, 2020. Crossref

  5. Faghidian S. Ali, Higher order mixture nonlocal gradient theory of wave propagation, Mathematical Methods in the Applied Sciences, 2020. Crossref

  6. Faghidian S. Ali, Two‐phase local/nonlocal gradient mechanics of elastic torsion, Mathematical Methods in the Applied Sciences, 2020. Crossref

  7. Abdelrahman A. A., Eltaher M. A., On bending and buckling responses of perforated nanobeams including surface energy for different beams theories, Engineering with Computers, 38, 3, 2022. Crossref

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