The pumpkin shape, although attractive in terms of pressure-carrying efficiency, has been found to be potentially unstable, with the result that several test balloons have been unable to pressurize into the desired axi-symmetric equilibrium configurations. Instead, they have settled into distorted configurations. The research presented in this presentation aims to provide computational techniques and solutions for the study of the shape and stability behavior of balloon structures.
A finite element model of a 10 m diameter pumpkin balloon with 145 lobes of approximately constant radius is set up. This model takes into account the tension-only behavior of the balloon skin, and contact between different parts of the surface is included in the model. The inflation of a single lobe, whose material is modelled as linear elastic, is simulated. The balloon is found to carry stresses biaxially. Eigenvalue buckling analyses are carried out to predict the critical buckling pressures and buckling modes. The balloon is found to have a 4-up, 4-down critical mode with a critical pressure of 2200 Pa. The sensitivity of these results to the material properties is studied.
A new finite element model is then set up with an initial geometric imperfection. With this model, geometrically nonlinear post-buckling analyses are carried out to simulate the response of the balloon beyond the critical pressure. Both global and local deformation modes are captured, followed by a thorough investigation of the stress distribution, the volume, and the energy variation of these deformed shapes. It is found that these stable distorted configurations enclose a larger volume compared with an unbuckled balloon.