Undesired Equilibria of Self-Deploying Pneumatic Envelopes

The advancement of materials and technology in thin lightweight films has generated great interest in deployable space structures for a variety of applications, including inflatable rovers, inflatable antennas, airbags to cushion landings, aerobots, and balloons. In this Note, we focus on two self-deploying structures: the zero-pressure natural shape balloon and the pumpkin shape superpressure balloon. The zero-pressure balloon has a long history of successful deployment. By contrast, the still experimental pumpkin shape superpressure balloon has a varied deployment history. Using a variational formulation and appropriate linear equality and inequality constraints, we explore the conditions that must be present for proper deployment and those that favor flawed deployment with the future aim to provide reliable design guidelines.