On the Existence of Equilibrium States of an Elastic Beam on a Nonlinear Foundation

Mohamed Elgindi, D. H.Y. Yen

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This paper concerns the existence and uniqueness of equilibrium states of a beam- column with hinged ends which is acted upon by axial compression and lateral forces and is in contact with a semi-infinite medium acting as a foundation. The problem is formulated as a fourth- order nonlinear boundary value problem in which the source of the nonlinearity comes from the lateral constraint (the foundation). Treating the equation of equilibrium as a nonlinear eigenvalue problem we prove the existence of a pair of eigenvalue/eigenfunction for each arbitrary prescribed energy level. Treating the equilibrium equation as a nonlinear boundary value problem we prove the existence and uniqueness of solution for a certain range of the acting axial compression force.

Original languageEnglish
Pages (from-to)193-198
Number of pages6
JournalInternational Journal of Mathematics and Mathematical Sciences
Issue number1
Publication statusPublished - 1993
Externally publishedYes



  • beam-column
  • elastic beam
  • Existence of equilibrium states
  • fourth-order nonlinear boundary value problem
  • nonlinear eigenvalue problems
  • variational methods

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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