Eringen's nonlocal theories of beams accounting for moderate rotations Academic Article uri icon


  • The primary objective of this paper is two-fold: (a) to formulate the governing equations of the Euler-Bernoulli and Timoshenko beams that account for moderate rotations (more than what is included in the conventional von Krmn strains) and material length scales based on Eringen's nonlocal differential model, and (b) develop the nonlinear finite element models of the equations. The governing equations of the Euler-Bernoulli and Timoshenko beams are derived using the principle of virtual displacements, wherein the Eringen's nonlocal differential model and modified von Krmn nonlinear strains are taken into account. Finite element models of the resulting equations are developed, and numerical results are presented for various boundary conditions, showing the effect of the nonlocal parameter on the deflections. 2014 Elsevier Ltd. All rights reserved.

published proceedings


author list (cited authors)

  • Reddy, J. N., & El-Borgi, S.

citation count

  • 85

complete list of authors

  • Reddy, JN||El-Borgi, Sami

publication date

  • September 2014