Nonlinear stress-driven nonlocal formulation of Timoshenko beams made of FGMs

Roghani, Mehran; Rouhi, H.

doi:10.1007/s00161-020-00906-z

Cited by 16 publications

(6 citation statements)

References 52 publications

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“…In this section, the nonlocal elasticity theory [10,11,[74][75][76][77] is used to introduce the small-scale effects in nanoscale beams.…”

Section: Nonlocal Elasticity Theorymentioning

confidence: 99%

“…In this section, the nonlocal elasticity theory [10,11,74–77] is used to introduce the small‐scale effects in nanoscale beams. From the nonlocal elasticity point of view, the fundamental concept is that the stress in a certain point is not only defined as a function of its own strain but also is affected by the strain fields of all other points of a flexible body.…”

Section: Nonlocal Elasticity Theorymentioning

confidence: 99%

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Nonlocalized thermal behavior of rotating micromachined beams under dynamic and thermodynamic loads

et al. 2021

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Rotating micromachined beams are one of the most practical devices with several applications from power generation to aerospace industries. Moreover, recent advances in micromachining technology have led to huge interests in fabricating miniature turbines, gyroscopes and microsensors thanks to their high quality/reliability performances. To this end, this article is organized to examine the axial dynamic reaction of a rotating thermoelastic nanobeam under a constantvelocity moving load. Using Eringen's nonlocal elasticity in conjunction with Euler-Bernoulli theory and Hamilton's principle, the governing equations are derived. It is assumed that the nanobeam is affected by thermal load and the boundary condition is simply supported. The Laplace transform approach is employed to solve the partial differential equations. A numerical example is presented to analyze the effects of the nonlocal parameter, rotation speed and velocity of the static moving load on the dynamic behavior of the system. The numerical results are graphically illustrated and analyzed to recognize the variations of field variables. Finally, in some special cases, our results are compared to those reported in the literature to demonstrate the reliability of the current model.

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“…In this section, the nonlocal elasticity theory [10,11,[74][75][76][77] is used to introduce the small-scale effects in nanoscale beams.…”

Section: Nonlocal Elasticity Theorymentioning

confidence: 99%

Section: Nonlocal Elasticity Theorymentioning

confidence: 99%

Nonlocalized thermal behavior of rotating micromachined beams under dynamic and thermodynamic loads

et al. 2021

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“…The stress-driven theory leads to well-posed structural problems (Romano and Barretta, 2017b), does not exhibit paradoxical results typical of alternative nonlocal beam models (Challamel and Wang, 2008;Demir and Civalek, 2017;Fernández-Sáez et al, 2016) and, in the last few years, has gained increasing popularity for consistency, robustness and ease of implementation. Stress-driven nonlocal theory of elasticity has been applied to several problems of nanomechanics, as witnessed by recent contributions regarding buckling (Oskouie et al, 2018b;Darban et al, 2020), bending (Oskouie et al, 2018a,c;Zhang et al, 2020a;Roghani and Rouhi), axial (Barretta et al, 2019a) and torsional responses (Barretta et al, 2018) of nano-beams and elastostatic behaviour of nano-plates (Barretta et al, 2019b;Farajpour et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

On the dynamics of nano-frames

Russillo

Failla

Alotta

et al. 2021

International Journal of Engineering Science

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In this paper, size-dependent dynamic responses of small-size frames are modelled by stressdriven nonlocal elasticity and assessed by a consistent finite-element methodology. Starting from uncoupled axial and bending differential equations, the exact dynamic stiffness matrix of a two-node stress-driven nonlocal beam element is evaluated in a closed form. The relevant global dynamic stiffness matrix of an arbitrarily-shaped small-size frame, where every member is made of a single element, is built by a standard finite-element assembly procedure. The Wittrick-Williams algorithm is applied to calculate natural frequencies and modes. The developed methodology, exploiting the one conceived for straight beams in [International Journal of Engineering Science 115, 14-27 (2017)], is suitable for investigating size-dependent free vibrations of small-size systems of current applicative interest in Nano-Engineering, such as carbon nanotube networks and polymer-metal micro-trusses.

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“…The stress-driven nonlocal approach has been successfully applied to a wide range of problems of nanotechnological interest (see e.g. Barretta et al, 2018b;Roghani, 2020;Barretta et al, 2018c;Pinnola, 2020;Oskouie et al, 2018;Barretta et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

Limit behaviour of Eringen’s two-phase elastic beams

Vaccaro

Pinnola

Sciarra

et al. 2021

European Journal of Mechanics - A/Solids

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In this paper, the bending behaviour of small-scale Bernoulli-Euler beams is investigated by Eringen's two-phase local/nonlocal theory of elasticity. Bending moments are expressed in terms of elastic curvatures by a convex combination of local and nonlocal contributions, that is a combination with non-negative scalar coefficients summing to unity. The nonlocal contribution is the convolution integral of the elastic curvature field with a suitable averaging kernel characterized by a scale parameter. The relevant structural problem, well-posed for non-vanishing local phases, is preliminarily formulated and exact elastic solutions of some simple beam problems are recalled. Limit behaviours of the obtained elastic solutions, analytically evaluated, studied and diagrammed, do not fulfill equilibrium requirements and kinematic boundary conditions. Accordingly, unlike alleged claims in literature, such asymptotic fields cannot be assumed as solutions of the purely nonlocal theory of beam elasticity. This conclusion agrees with the known result which the elastic equilibrium problem of beams of engineering interest formulated by Eringen's purely nonlocal theory admits no solution.

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Nonlinear stress-driven nonlocal formulation of Timoshenko beams made of FGMs

Cited by 16 publications

References 52 publications

Nonlocalized thermal behavior of rotating micromachined beams under dynamic and thermodynamic loads

Nonlocalized thermal behavior of rotating micromachined beams under dynamic and thermodynamic loads

On the dynamics of nano-frames

Limit behaviour of Eringen’s two-phase elastic beams

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