A possible alternative to the lenticular configuration, the concept of a torus-less pressurized membrane antenna with an exact parabolic center, is introduced. For a characteristic symmetric configuration, three membrane regions are identified: the parabolic reflector center, the (wrinkled) perimeter that suspends it, and a transition zone between. Via an analysis of the pressurization kinematics, the last of the three is seen as critical. Structural economy and optimization are considered, and a design paradigm is established and demonstrated. It is also shown that there can exist mechanically sound pressurized membrane shapes for which no strain-free initial configurations correspond. The study is restricted to the pressurized membrane itself: no application-specific system integration issues are addressed.
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