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
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.
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