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عنوان فارسی مقاله:
خم و کمانش گرادیان فشار غیر محلی پرتوهای الاستیک
عنوان انگلیسی مقاله:
Bending and buckling of nonlocal strain gradient elastic beams
سال انتشار : 2016
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مقدمه انگلیسی مقاله:
1. Introduction
. Introduction Engineering structures such as beams, plates and shells have been widely used in micro- and nano-sized sensors, actuators, atomic force microscopes. In these applications, size effects of material properties are observed at small sizes both in experimental works [1–4] and in numerical simulations [5–7]. The aforementioned works show that the materials exhibit either stiffening behaviors or softening behaviors in comparison to the bulk cases. Therefore, continuum theories that can capture the size effects of materials at small sizes have attracted considerable attention in the research communities with the view toward a better understanding and characterization of materials. Based on the concept that the stress at a reference point is not only a function of the reference point, but also the strain at all points of the body, Eringen [8] developed an elasticity theory for the applications in surface waves. With the emerging of carbon nanotubes and graphene sheets, this theory have been extended to the study of the static and dynamic behaviors of structures in terms of rods [9–14], beams [14–25], plates [26–33] and shells [34–38]. For more details, the interested reader may refer to the recent reviews by Arash and Wang [39] and Eltaher, et al. [40]. In general, the use of this theory results in the softening effect when it is compared with the classical elasticity theory. However, two issues violate the softening phenomena. The first issue is that the bending solutions of nonlocal models in some cases are found to be the same as the classical solutions. In other words, the size effects vanish for cantilever beams subjected to concentrated forces [41]. To address this issue, Challamel and Wang [42] proposed a gradient elastic model as well as an integral nonlocal elastic model that is based on combining the local and the nonlocal curvatures in the constitutive relation. After this, several fresh ideas are raised to clarify this issue [16,43–46]. For example, Khodabakhshi and Reddy [43] developed a unified integro-differential nonlocal elasticity model and used this model to the bending of Euler–Bernoulli beams. Fernández-Sáez et al. [46] investigated the bending problems of Euler–Bernoulli beams using the Eringen integral constitutive equation. The closed-form bending solutions of Euler–Bernoulli beams and Timoshenko beams subjected to different loading and boundary conditions were carried out by Tuna and Kirca [16]. It appears that the first issue can be solved with the aid of the integro-differential nonlocal elasticity theory. The second issue is that one can only obtain a few natural frequencies of free vibrations of cantilever beams and that the counterintuitive stiffening effect is observed. This issue has been analytically solved by Xu et al. [47] using the weighted residual approaches (WRAs). In their work, they reformulated the variational-consistent boundaryconditions, and presented the closed-form frequency solutions for Euler–Bernoulli beams and Timoshenko beams. The solutions of the above-mentioned issues demonstrate that, when one uses the nonlocal elasticity, the boundary conditions should be correctly employed rather than simply replacing the classical force resultants by the nonclassical force resultants in the equilibrium equations.
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کلمات کلیدی:
A nonlocal beam theory for bending, buckling, and ... - ScienceDirect www.sciencedirect.com/science/article/pii/S0020722511002412 by HT Thai - 2012 - Cited by 202 - Related articles Dec 22, 2011 - A nonlocal shear deformation beam theory is proposed for bending, buckling, and vibration of nanobeams using the nonlocal differential ... A general nonlocal beam theory: Its application to nanobeam bending ... www.sciencedirect.com/science/article/pii/S1386947709001714 by M Aydogdu - 2009 - Cited by 311 - Related articles In the present study, a generalized nonlocal beam theory is proposed to study bending, buckling and free vibration of nanobeams. Nonlocal constitutive ... Bending analysis of microtubules using nonlocal Euler–Bernoulli ... www.sciencedirect.com/science/article/pii/S0307904X10004142 by Ö Civalek - 2011 - Cited by 157 - Related articles It is also accepted that some mechanical properties such as vibration, bending and buckling of beam like micro structures based on nonlocal elasticity theory are ... A nonlocal beam theory for bending, buckling, and ... - ResearchGate https://www.researchgate.net/.../233910821_A_nonlocal_beam_theory_for_bending_bu... A nonlocal shear deformation beam theory is proposed for bending, buckling, and vibration of nanobeams using the nonlocal differential constitutive relations of ... Nonlocal theories for bending, buckling and vibration ... - ResearchGate https://www.researchgate.net/.../222907475_Nonlocal_theories_for_bending_buckling_... Various available beam theories, including the Euler–Bernoulli, Timoshenko, Reddy, and Levinson beam theories, are reformulated using the nonlocal ... [PDF]analysis of vibration and buckling problems in non-local beam ... - Cimec www.cimec.org.ar/ojs/index.php/mc/article/view/4781/4712 by MT Piovan - Related articles as a thin-walled beam with motion in three axes, i.e. bending in two directions ... uncertainty associated to the non-local parameters in the buckling response and ...
