Representation formula for the critical points of the tadjbakhsh-odeh functional and its application

Kohtaro Watanabe, Izumi Takagi

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In order to study the buckled states of an elastic ring under uniform pressure, Tadjbakhsh and Odeh [14] introduced an energy functional which is a linear combination of the total squared curvature (elastic energy) and the area enclosed by the ring. We prove that the minimizer of the functional is not a disk when the pressure is large, and its curvature can be expressed by Jacobian elliptic cn(·) function. Moreover, the uniqueness of the minimizer is proven for certain range of the pressure.

Original languageEnglish
Pages (from-to)331-372
Number of pages42
JournalJapan Journal of Industrial and Applied Mathematics
Volume25
Issue number3
DOIs
Publication statusPublished - 2008 Oct

Keywords

  • Structure of the critical point
  • Tadjbakhsh-odeh functional
  • Total squared curvature
  • Uniqueness of the minimizer

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Representation formula for the critical points of the tadjbakhsh-odeh functional and its application'. Together they form a unique fingerprint.

Cite this