Analysis of a gradient-elastic beam on Winkler foundation and applications to nano-structure modelling

D. M. Manias, T. K. Papathanasiou, S. I. Markolefas, E. E. Theotokoglou

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

An equation of motion governing the response of a first strain gradient beam, including the effect of a Winkler elastic foundation, is derived from the Hamilton-Lagrange principle. The model is based on Mindlin's gradient elasticity theory, while the Euler-Bernoulli assumption for slender beams is adopted. Higher-continuity Hermite Finite Elements are presented for the numerical solution of related Initial-Boundary Value (IBV) problems. In the static case an analytical solution is derived and the convergence characteristics of the proposed Finite Element formulation are validated against the exact response of the configuration. Several examples are presented using "equivalent beam" data for Carbon Nanotubes (CNT's) and the effect on the Winkler foundation is studied. Finally, applicability of the derived model for the simulation of micro-structures, as for example CNT's or Microtubules, is discussed.

Original languageBritish English
Pages (from-to)45-58
Number of pages14
JournalEuropean Journal of Mechanics, A/Solids
Volume56
DOIs
StatePublished - Mar 2016

Keywords

  • Euler-Bernoulli beams
  • Gradient elasticity
  • Winkler foundation

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