A general nonlocal nonlinear model for buckling of nanobeams

Samir A. Emam

Research output: Contribution to journalArticlepeer-review

89 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)6929-6939
Number of pages11
JournalApplied Mathematical Modelling
Issue number10-11
Publication statusPublished - Jun 1 2013


  • Analytical solution
  • Nanobeams
  • Nonlocal elasticity
  • Postbuckling

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics


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