Multiple scales solution for a beam with a small bending stiffness

V. Denoël, E. Detournay

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


This paper considers the problem of a beam with a small bending stiffness, within the framework of a nonlinear beam model that includes both the classical cable and the linear beam as limiting cases. This problem, treated as a perturbation of the catenary solution, is solved with the multiple scales method. The resulting expressions of the beam deflection and of the internal forces, as well as those obtained with the more commonly applied matched asymptotics method, are compared with numerical results. This comparison indicates that a better accuracy can be achieved with the multiple scales approach, for a similar computational effort. These results also suggest that application of the multiple scales method to the solution of beam problems involving boundary layers extend the range of values of the small parameter, for which accurate analytical solutions can be obtained by a perturbation technique.

Original languageEnglish (US)
Article number006001QEM
Pages (from-to)69-77
Number of pages9
JournalJournal of Engineering Mechanics
Issue number1
StatePublished - Jan 2010


  • Boundary layer
  • Catenary
  • Matched asymptotics
  • Multiple scales
  • Rod theory
  • Small bending stiffness


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