  Liquid crystal elastomers contract along their director on heating and
recover on cooling, offering great potential as actuators and artificial
muscles. If a flat sheet is programmed with a spatially varying director
pattern, it will actuate into a curved surface, allowing the material to act as
a strong machine such as a grabber or lifter. Here we study the actuation of
programmed annular sheets which, owing to their central hole, can sidestep
constraints on area and orientation. We systematically catalogue the set of
developable surfaces encodable via axisymmetric director patterns, and uncover
several qualitatively new modes of actuation, including cylinders, irises, and
everted surfaces in which the inner boundary becomes the outer boundary after
actuation. We confirm our designs with a combination of experiments and
numerics. Many of our actuators can re-attain their initial inner or outer
radius upon completing actuation, making them particularly promising, as they
can avoid potentially problematic stresses in their activated state even when
fixed onto a frame or pipe.
