Buckling of a nonlinear elastic rod

W. E. Olmstead*, D. J. Mescheloff

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The buckling of a pin-ended slender rod subjected to a horizontal end load is formulated as a nonlinear boundary value problem. The rod material is taken to be governed by constitutive laws which are nonlinear with respect to both bending and compression. The nonlinear boundary value problem is converted to a suitable integral equation to allow the application of bounded operator methods. By treating the integral equation as a bifurcation problem, the branch points (critical values of load) are determined and the existence and form of nontrivial solutions (buckled states) in the neighborhood of the branch points is established. The integral equation also affords a direct attack upon the question of uniqueness of the trivial solution (unbuckled state). It is shown that, under certain conditions on the material properties, only the trivial solution is possible for restricted values of the load. One set of conditions gives uniqueness up to the first branch point.

Original languageEnglish (US)
Pages (from-to)609-634
Number of pages26
JournalJournal of Mathematical Analysis and Applications
Volume46
Issue number3
DOIs
StatePublished - Jun 1974

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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