Partial plane contact of an elastic curved beam pressed by a flat surface

Joseph M. Block, Leon M Keer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


The normal contact of a frictionless, elastic curved beam indented by a flat, rigid surface is solved using a Michell-Fourier series expansion, which satisfies the mixed boundary value problem resulting from partial contact. When the contact region is small compared to the radius of curvature of the beam, semi-analytical solutions are obtained by exploiting dual series equation techniques. The relation between the level of loading and the extent of contact, as well as stress on the surface, are found for plane strain. The elasticity results extend Hertz line contact to finite thickness, curved beams. As the beam becomes thin, beam theory type behavior is recovered. The results may have application to finite-thickness wavy surfaces, cylindrical structures, or pressurized seals.

Original languageEnglish (US)
Pages (from-to)60-64
Number of pages5
JournalJournal of Tribology
Issue number1
StatePublished - Jan 1 2007


  • Dual series
  • Elastic contact
  • Michell solution
  • Mixed boundary conditions

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Surfaces and Interfaces
  • Surfaces, Coatings and Films


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