Stability analysis of nanobeams placed in electromagnetic field using a finite element method
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ORIGINAL PAPER
Stability analysis of nanobeams placed in electromagnetic field using a finite element method Ömer Civalek 1
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Büşra Uzun 2
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Mustafa Özgür Yaylı 2
Received: 5 March 2020 / Accepted: 27 October 2020 # Saudi Society for Geosciences 2020
Abstract In this work, the buckling analysis of the nanobeams placed in electromagnetic field is presented via a nonlocal finite element method based on Eringen’s nonlocal elasticity theory. The governing differential equation is derived by implementing minimum total potential energy principle. A finite element method is proposed for solution of nonlocal buckling of nanobeam placed in electromagnetic field. The contribution of this article is the use of interpolation functions and the nonlocal elasticity theory to form the stiffness matrices and geometric stiffness matrices of the electromagnetic nanobeam for buckling analysis. A detailed study is performed to indicate the influences of some parameters such as Hartmann parameter (Ha), mode number (n), nonlocal parameter (e0a), length of nanobeam (L), and boundary conditions on the buckling loads of Euler-Bernoulli nanobeams. The values of buckling load of electromagnetic nanobeams are obtained via a finite element solution, examined through several numerical examples, and demonstrated by tables and graphs. Keywords Electromagnetic field . Nonlocal elasticity theory . Stability . Finite element method . Nanobeam
Introduction The advancement of technology in such a way that it can interfere with the nanoscale has led to the emergence of research related to the properties of the nanoscale materials/ structures and their usage areas. In terms of mechanical, physical, chemical, and electrical properties, nano-sized materials/ structures give superior results compared to the macro dimensions we are used to. By the virtue of these noteworthy features, nanostructures have been used in continuum mechanics models as well. However, atomistic modeling and Responsible Editor: Amjad Kallel * Büşra Uzun [email protected] Ömer Civalek [email protected] Mustafa Özgür Yaylı [email protected] 1
Research Center for Interneural Computing University, China Medical University, Taichung, Taiwan
2
Department of Civil Engineering, Faculty of Engineering, Bursa Uludag University, Görükle Campus, 16059 Bursa, Turkey
experiments showed that there are deficiencies in the explanation of the properties and behaviors of nanostructures with classical continuum theories. The reason for these deficiencies is that classical theories do not include the small-scale parameters, which is critical for more properly understanding of characteristic features of ultra-small structures, and represents the interaction between atoms and molecules. Therefore, the nonlocal elasticity theory introduced by Eringen (1983) has been a frequently used approach in the mechanical (static, dynamic) analysis of nano-sized structures. Nanobeams (Civalek and Demir 2011; Demir and Civalek 2017a; Uzun et al. 2018; Uzun and Civalek 2019a, 2019b; Ebrahimi and Nasi
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