https://doi.org/10.1140/epjp/s13360-020-00661-9
Regular Article
Nonlinear flexure of Timoshenko–Ehrenfest nano-beams via nonlocal integral elasticity
1
Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
2
Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
3
Department of Civil Engineering, Sharif University of Technology, Tehran, Iran
4
Institute for Nanoscience and Nanotechnology, Sharif University of Technology, Tehran, Iran
b faghidian@gmail.com, faghidian@srbiau.ac.ir
Received:
2
April
2020
Accepted:
31
July
2020
Published online:
9
August
2020
Nonlinear flexural behavior of elastic nano-beams under static loads is investigated in the framework of the Eringen’s nonlocal integral elasticity. The integro-differential and boundary conditions of equilibrium for inflected Timoshenko–Ehrenfest elastic beams with von Kármán nonlinear strains are established by using the minimum total potential energy principle. Eringen’s nonlocal differential law, consequent (but not equivalent) to Eringen’s nonlocal integral convolution, is well established to be inconsistent when applied to bounded domains of nano-mechanics interest. Accordingly, nonlocal integral elasticity formulation is utilized to capture scale effects in the nonlinear flexure of nano-beams. An analytical series solution in terms of Chebyshev polynomials is proposed to suitably approximate the displacement field of inflected nano-beams. Selected case studies of applicative interest are investigated, and the approximated nonlinear solutions of nonlocal nano-beams are detected. The demonstrated benchmark examples can be effectively employed in the assessment of beam-type elements of nano-electromechanical systems.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
