| A mathematical model for a tendon-reinforced piecewise-isotropic thin inflated membrane subjected to a hydrostatic pressure load is developed. While the existence results established herein apply to a large scientific balloon, this model could be applied to other inflatable structures. A stress analysis is performed on a balloon without caps and on a balloon with caps. External caps are treated as an additional film thickness, leading to the aforementioned piecewise-isotropic membrane. The model includes contributions due to a position dependent hydrostatic pressure, relaxed film strain, film and tendon weight, and inextensible tendons. A variational principle with constraints is applied to a quasiconvex continuous Lagrangian in the case of a balloon without caps, and a quasiconvex Caratheodory Lagrangian in the case of a balloon with caps. Using direct methods in the calculus of variations, rigorous existence theorems for the balloon systems are established. |
