Abstract
Buckling analysis of nanobeams is investigated using nonlocal continuum beam models of the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), and Levinson beam theory (LBT). To this end, Eringen’s equations of nonlocal elasticity are incorporated into the classical beam theories for buckling of nanobeams with rectangular cross-section. In contrast to the classical theories, the nonlocal elastic beam models developed here have the capability to predict critical buckling loads that allowing for the inclusion of size effects. The values of critical buckling loads corresponding to four commonly used boundary conditions are obtained using state-space method. The results are presented for different geometric parameters, boundary conditions, and values of nonlocal parameter to show the effects of each of them in detail. Then the results are fitted with those of molecular dynamics simulations through a nonlinear least square fitting procedure to find the appropriate values of nonlocal parameter for the buckling analysis of nanobeams relevant to each type of nonlocal beam model and boundary conditions.analysis.
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This paper was recommended for publication in revised form by Editor Maenghyo Cho
Reza Ansari received his Ph.D. degree in Mechanical Engineering from University of Guilan, Iran, in 2008. Dr. Ansari is currently an associated Professor at the Department of Mechanical Engineering at University of Guilan. His research interests include mathematical modeling and analysis of mechanical behavior of engineering structure and smart structures, probabilistic analysis, and computational nanomechanics.
Saeid Sahmani received his B.S. degree in Mechanical Engineering from University of Guilan, Iran, in 2006. He then received his M.S. degree from Iran University of Science and Technology (IUST) in 2009. He is now continuing his study as Ph.D. student in the research field of nanomechanics.
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Sahmani, S., Ansari, R. Nonlocal beam models for buckling of nanobeams using state-space method regarding different boundary conditions. J Mech Sci Technol 25, 2365–2375 (2011). https://doi.org/10.1007/s12206-011-0711-6
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DOI: https://doi.org/10.1007/s12206-011-0711-6