We present an analysis of the finite deformation of an annular memberane induced by the rotation of a rigid hub. The memberane is partly wrinkled for certain combinations of hub radius and rotation angle. For a particular strain-energy function of harmonic type, we obtain solutions that are analytical in the sense that the problem is reduced to an algebraic system in three parameters. Solutions of this system are used to characterize various properties of the deformation, including the equilibrium torque-twist relation.
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