Translator Disclaimer
October 2008 Representation Formula for the Critical Points of the Tadjbakhsh--Odeh Functional and its Application
Kohtaro Watanabe, Izumi Takagi
Japan J. Indust. Appl. Math. 25(3): 331-372 (October 2008).

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 $\cn({}\cdot{})$ function. Moreover, the uniqueness of the minimizer is proven for certain range of the pressure.

Citation

Download Citation

Kohtaro Watanabe. Izumi Takagi. "Representation Formula for the Critical Points of the Tadjbakhsh--Odeh Functional and its Application." Japan J. Indust. Appl. Math. 25 (3) 331 - 372, October 2008.

Information

Published: October 2008
First available in Project Euclid: 5 June 2009

zbMATH: 1157.49044
MathSciNet: MR2479130

Rights: Copyright © 2008 The Japan Society for Industrial and Applied Mathematics

JOURNAL ARTICLE
42 PAGES


SHARE
Vol.25 • No. 3 • October 2008
Back to Top