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

Mohamed Elgindi, D. H.Y. Yen

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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
Volume16
Issue number1
DOIs
Publication statusPublished - 1993
Externally publishedYes

Fingerprint

Nonlinear Boundary Value Problems
Equilibrium State
Lateral
Compression
Fourth-order Boundary Value Problem
Nonlinear Eigenvalue Problem
Existence and Uniqueness of Solutions
Energy Levels
Eigenfunctions
Existence and Uniqueness
Nonlinearity
Contact
Eigenvalue
Arbitrary
Range of data

Keywords

  • 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)

Cite this

On the Existence of Equilibrium States of an Elastic Beam on a Nonlinear Foundation. / Elgindi, Mohamed; Yen, D. H.Y.

In: International Journal of Mathematics and Mathematical Sciences, Vol. 16, No. 1, 1993, p. 193-198.

Research output: Contribution to journalArticle

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