Structural analysis of pneumatic envelopes: Variational formulation and optimization-based solution process

Large super-light structural systems that for functional reasons require large surfaces are composed at least in part of structural membranes. The underconstrained nature of such structural membranes poses analytical challenges, but also provides design opportunities that are not commonly found in other structural systems that require the arsenal of solid-mechanics analytical tools for the assessment of design validity and performance. Overcoming some of the challenges that are posed by the underconstrained nature of such systems is an important ingredient in the development process for gossamer spacecraft. Our approach is a variational formulation of the analytical problem in conjunction with optimization techniques in the solution process. The optimization-based solution process avoids convergence problems that are encountered in the implicit solution process of finite element formulations of these underconstrained structures. To illustrate our approach, we carry out a structural analysis of a pumpkin balloon. Our formulation incorporates wrinkling of the balloon film and structural lack of fit between the skin and the tendon in the unloaded, that is, unstrained, structure. Our results on pumpkin balloons suggest the possibility of similar success if our methods are applied to other pneumatic envelopes.