Size-dependent bending analysis of Kirchhoff nano-plates based on a modified couple-stress theory including surface effects

M. Shaat, F. F. Mahmoud, X. L. Gao, Ahmed F. Faheem

Research output: Contribution to journalArticlepeer-review

166 Scopus citations

Abstract

In the present work, a new Kirchhoff plate model is developed using a modified couple-stress theory to study the bending behavior of nano-sized plates, including surface energy and microstructure effects. The surface elasticity theory of Gurtin and Murdoch is used to model the surface energy effects, into the framework of the modified couple-stress theory of elasticity. Newtonian continuum mechanics approach is used to derive the differential form of the equilibrium equations for the modified Kirchhoff plate theory. The modified plate rigidity is derived to express the size effects in nanoplates. Presence of a length scale parameter, in the context of the modified couple-stress theory, enables us to express the size effect in nano-scale structures. In addition, an intrinsic length scale parameter is determined as a result of taking surface energy effects into account. In order to illustrate the model, an analytical solution of the static bending of a simply supported nano-plate has been derived. For ultra-thin plates it is noticed that the microstructure effects on bending rigidity and deflection, through the application of the modified-couple stress theory, is highly significant than that caused by the surface energy effect.

Original languageBritish English
Pages (from-to)31-37
Number of pages7
JournalInternational Journal of Mechanical Sciences
Volume79
DOIs
StatePublished - Feb 2014

Keywords

  • Couple stress theory
  • Kirchhoff nano-plates
  • Size effect
  • Size-dependent model
  • Surface elasticity

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