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A general nonlocal nonlinear model for buckling of nanobeams
Faculty
Science
Year:
2013
Type of Publication:
Article
Pages:
6929-6939
Authors:
Emam, Samir A
DOI:
10.1016/j.apm.2013.01.043
Journal:
APPLIED MATHEMATICAL MODELLING ELSEVIER SCIENCE INC
Volume:
37
Research Area:
Engineering; Mathematics; Mechanics
ISSN
ISI:000320568200028
Keywords :
Nanobeams, Postbuckling, Analytical solution, Nonlocal elasticity
Abstract:
This study presents a unified model for the nonlocal response of nanobeams in buckling and postbuckling states. The formulation is suitable for the classical Euler Bernoulli, first-order Timoshenko, and higher-order shear deformation beam theories. The small-scale effect is modeled according to the nonlocal elasticity theory of Eringen. The equations of equilibrium are obtained using the principle of virtual work. The stress resultants are developed taking into account the nonlocal effect. Analytical solutions for the critical buckling load and the amplitude of the static nonlinear response in the postbuckling state are obtained. It is found out that as the nonlocal parameter increases, the critical buckling load reduces and the amplitude of buckling increases. Numerical results showing variation of the critical buckling load and the amplitude of buckling with the nonlocal parameter and the length-to-height ratio for simply supported and clamped clamped nanobeams are presented. (C) 2013 Elsevier Inc. All rights reserved.
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