TY - JOUR
T1 - Representation formula for the critical points of the tadjbakhsh-odeh functional and its application
AU - Watanabe, Kohtaro
AU - Takagi, Izumi
PY - 2008/10
Y1 - 2008/10
N2 - 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.
AB - 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.
KW - Structure of the critical point
KW - Tadjbakhsh-odeh functional
KW - Total squared curvature
KW - Uniqueness of the minimizer
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U2 - 10.1007/BF03168554
DO - 10.1007/BF03168554
M3 - Article
AN - SCOPUS:58149393357
VL - 25
SP - 331
EP - 372
JO - Japan Journal of Industrial and Applied Mathematics
JF - Japan Journal of Industrial and Applied Mathematics
SN - 0916-7005
IS - 3
ER -