دانلود رایگان مقاله لاتین کمانش گرادیان فشار غیر محلی پرتو الاستیک از سایت الزویر
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
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:
Nonlocal strain gradient based wave dispersion behavior of smart ... iopscience.iop.org/article/10.1088/2053-1591/aa55b5/meta by F Ebrahimi - 2017 Feb 3, 2017 - Eringen A C 1972 Linear theory of nonlocal elasticity and dispersion of ... A higher-order nonlocal strain gradient plate model for buckling of ... BUCKLING OF COMPOSITE NONLOCAL OR GRADIENT ... www.worldscientific.com › ... › Available Issues › Volume 11, Issue 06 by N CHALLAMEL - 2011 - Cited by 8 - Related articles The buckling of an axially loaded elastic composite beam with a nonlocal core or a ... (2015) A higher-order nonlocal elasticity and strain gradient theory and its ... Higher order nonlocal strain gradient approach for wave ... https://www.mii.lt/na/issues/NA_1904/NA19410.pdf by B Yakaiah - 2014 - Cited by 1 - Related articles Aug 25, 2014 - the nanorod obtained from the nonlocal strain gradient models are ... Keywords: nonlocal elasticity, nanorod, wave propagation, critical wave number. ..... J.N. Reddy, S.D. Pang, Nonlocal theories for bending,buckling and ... Strain gradient elasticity and modified couple stress models for ... - ijeas ijeas.akdeniz.edu.tr/wp-content/uploads/2016/09/yayin17.pdf for buckling analysis of axially loaded micro-scaled beams ... After this, modified couple stress, nonlocal elasticity and strain gradient elasticity theories have ... Nonlocal strain gradient theory for damping vibration analysis of ... journals.sagepub.com/doi/abs/10.1177/1077546316678511 by F Ebrahimi - Related articles PDF download for Nonlocal strain gradient theory for damping vibration analysis ... is investigated based on nonlocal strain gradient elasticity theory and a higher order ... Ebrahimi F, Barati MR (2016d) Buckling analysis of nonlocal third-order ... Variational principles for buckling and vibration of MWCNTs modeled ... link.springer.com/article/10.1007/s10483-014-1855-6 by X Xu - 2014 - Cited by 7 - Related articles Feb 26, 2014 - Variational principles for the buckling and vibration of multi-walled ... variational principle strain gradient theory buckling vibration carbon ...
