Closed-form solutions in stress-driven two-phase integral elasticity for bending of functionally graded nano-beams

Barretta, Raffaele; Fabbrocino, Francesco; Luciano, Raimondo; Sciarra, Francesco Marotti de

doi:10.1016/j.physe.2017.09.026

Cited by 99 publications

(45 citation statements)

References 51 publications

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“…The mixture stress-driven integral model (MStreDM) is applied to Timoshenko nano-beams. MStreDM is the generalization to stubby beams of a previous constitutive version formulated in [42] for Bernoulli-Euler nanobeams in which the flexural curvature field ‰(x) is expressed by the following two-phase law:…”

Section: Mixture Stress-driven Integral Model For Timoshenko Beamsmentioning

confidence: 99%

“…On the contrary, the stress-driven theory does not su er the limiting behavior of strain-driven formulations as the local fraction tends to zero. The stress-driven model has been adopted in various problems such as bending of functionally graded nano-beams [42,43] and nonlocal thermoelastic behavior of nano-beams [44]. Such a model provides a sti ening structural behavior in accordance with experimental evidences [15,45].…”

Section: Introductionmentioning

confidence: 99%

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A stress-driven local-nonlocal mixture model for Timoshenko nano-beams

Barretta

Caporale

Faghidian

et al. 2019

Composites Part B: Engineering

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A well-posed stress-driven mixture is proposed for Timoshenko nano-beams.The model is a convex combination of local and nonlocal phases and circumvents some problems of ill-posedness emerged in strain-driven Eringen-like formulations for structures of nanotechnological interest. The nonlocal part of the mixture is the integral convolution between stress field and a biexponential averaging kernel function characterized by a scale parameter.The stress-driven mixture is equivalent to a di erential problem equipped with constitutive boundary conditions involving bending and shear fields.Closed-form solutions of Timoshenko nano-beams for selected boundary and loading conditions are established by an e ective analytical strategy. The numerical results exhibit a sti ening behavior in terms of scale parameter.

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Section: Mixture Stress-driven Integral Model For Timoshenko Beamsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A stress-driven local-nonlocal mixture model for Timoshenko nano-beams

Barretta

Caporale

Faghidian

et al. 2019

Composites Part B: Engineering

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“…For the present research, nonisothermal model [29] is of interest. But, when the nonlocal procedures are concerned, inclusion of the shift of neutral surface is much less common; for the isothermal strain gradient formulation see [35][36][37][38] and for the integral based [39]. For the gradient based thermoelastic beams including hygro effects, see [15].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams

Barretta

Čanađija

Sciarra

2019

Composite Structures

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An effective nonlocal integral formulation for functionally graded Bernoulli-Euler beams in nonisothermal environment is developed. Both thermal and mechanical loadings are accounted for. The proposed model, of stress-driven integral type, is shown to be governed by a thermodynamically consistent differential problem with proper constitutive boundary conditions. The new thermoelastic strategy is illustrated by investigating a set of examples. It is demonstrated that in nonisothermal statically indeterminate problems rather complex structural behaviours can appear and that both the shift of the neutral surface and nonlocality have a dominating influence at small-scales.

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“…Based on nonlocal beam theory, the static bending, buckling, vibration, and wave properties of single-/double-walled CNTs have been studied systematically [17][18][19][20][21]. In recent years, the nonlocal mechanics of elastic nanobeams have undergone rapid progress, with a lot of newly-developed theories, e.g., strain-driven and stress-driven nonlocal integral elasticity theory [22][23][24], two-phase integral elasticity theory [25], nonlocal strain gradient elasticity theory [26][27][28], and modified nonlocal strain gradient elasticity theory [29,30].…”

Section: Introductionmentioning

confidence: 99%

Vibration Analysis of Fluid Conveying Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory by Spectral Element Method

Wang

2019

Nanomaterials

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In this work, we applied the spectral element method (SEM) to analyze the dynamic characteristics of fluid conveying single-walled carbon nanotubes (SWCNTs). First, the dynamic equations for fluid conveying SWCNTs were deduced based on the nonlocal Timoshenko beam theory. Then, the spectral element formulation was established for a free/forced vibration analysis of fluid conveying SWCNTs by introducing discrete Fourier transform. Furthermore, the proposed method was validated using several comparison examples. Finally, the natural frequencies and dynamic responses of a simply-supported fluid conveying SWCNTs were calculated by the SEM, considering different internal fluid velocities and small-scale parameters (SSPs). The effects of fluid velocity and SSPs on the dynamic characteristics of SWCNTs conveying fluid were revealed by the numerical results. Compared with other methods, the SEM shows high accuracy and efficiency.

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Closed-form solutions in stress-driven two-phase integral elasticity for bending of functionally graded nano-beams

Cited by 99 publications

References 51 publications

A stress-driven local-nonlocal mixture model for Timoshenko nano-beams

A stress-driven local-nonlocal mixture model for Timoshenko nano-beams

Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams

Vibration Analysis of Fluid Conveying Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory by Spectral Element Method

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