Bending Analysis of Carbon Nanotubes Based on Analytical Nonlocal Timoshenko Beam Model

Abstract:

Based on nonlocal elastic continuum theory, a new mathematical model and analytical solutions for nonlocal Timoshenko beam model (ANT) is established according to Hamiltons principle. Shear deformation and nonlocal effect are considered in the ANT model. The new ANT equilibrium equations and boundary conditions are derived for bending analysis of carbon nanotube (CNT). The bending behaviors of CNT with simply supported and cantilever boundary conditions are solved and discussed. The ANT deflection solutions demonstrate that the CNT stiffness is enhanced by the presence of nonlocal stress effects. Furthermore, the new ANT models concluded verifiable bending behaviors for a cantilever CNT with point load at the free end, which depends on the strength of nonlocal stress. This new conclusion reverts the current understanding according to the common nonlocal models adopted today, that the deflection in this case is indifferent to stress nonlocality and thus it surprising behaves like a macro beam with classical beam bending solution without size effect.

• Periodical: Applied Mechanics and Materials (Volumes 444-445)
• Pages: 202-208
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.444-445.202
• Online since: October 2013
• Authors: Yang Yang
• Keywords: Carbon Nanotube (CN), Nonlocal Stress, Shear Deformation, Timoshenko Nanobeam

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