Representation Formula for the Critical Points of the Tadjbakhsh--Odeh Functional and its Application

Watanabe, Kohtaro; Takagi, Izumi

Japan J. Indust. Appl. Math., Tome 25 (2008) no. 1, p. 331-372 / Harvested from Project Euclid

Résumé

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.

Publié le : 2008-10-15
Classification: Tadjbakhsh--Odeh functional, structure of the critical point, uniqueness of the minimizer, total squared curvature

@article{1244209046,
     author = {Watanabe, Kohtaro and Takagi, Izumi},
     title = {Representation Formula for the Critical Points of the Tadjbakhsh--Odeh Functional and its Application},
     journal = {Japan J. Indust. Appl. Math.},
     volume = {25},
     number = {1},
     year = {2008},
     pages = { 331-372},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1244209046}
}

Watanabe, Kohtaro; Takagi, Izumi. Representation Formula for the Critical Points of the Tadjbakhsh--Odeh Functional and its Application. Japan J. Indust. Appl. Math., Tome 25 (2008) no. 1, pp.  331-372. http://gdmltest.u-ga.fr/item/1244209046/