Clefted Equilibrium Shapes of Superpressure Balloon Structures

This thesis presents a numerical and analytical study of the clefted equilibrium shape of superpressure balloon structures. Lobed superpressure balloons have shown a tendency to deploy into unexpected asymmetric shapes, hence their design has to strike a balance between the lower stresses achieved by increasing lobing and the risk of incomplete deployment. Extensive clefting is a regular feature of balloons that are incompletely inflated, and is regularly seen during launch and ascent. Our particular interest in the research is in clefts that remain once a balloon has reached its float altitude and is fully pressurized. A simplified simulation technique for orthotropic viscoelastic membranes is presented in the thesis. Wrinkling is detected by a combined stress-strain criterion and an iterative scheme searches for the wrinkle angle using a pseudoelastic material stiffness matrix based on a nonlinear viscoelastic constitutive model. This simplified model has been implemented in ABAQUS/Explicit and is able to compute the behavior of a membrane structure by superposition of a small number of response increments. The model has been tested against a published solution for a time-independent isotropic membrane under simple shear and also against experimental results on StratoFilm 420 under simple shear. A fully three-dimensional finite element model of balloon structures incorporating wrinkling and frictionless contact, able to simulate the shapes taken up by lobed superpressure balloons during the final stages of their ascent has been established. Two different methods have been considered to predict the clefts: (i) deflation and inflation method and (ii) constraint shift method. In method (i), the starting configuration is obtained by deflating an initially symmetric balloon subject to uniform pressure. The deflation simulation is continued until the differential pressure at the bottom of the balloon has become negative, at which point the balloon is extensively clefted. The balloon is then inflated by increasing the bottom pressure while maintaining a uniform vertical ressure gradient, and the evolution of the shape and stress distribution of the balloon is studied. Two different designs of uperpressure balloons are investigated: a flat facet balloon and a ighly lobed balloon. It is found that the flat facet balloon follows essentially the same path during deflation and inflation, and hence will deploy into a unique, symmetric shape. For the lobed balloon it is found that it follows different paths during deflation and inflation, and deploys into an alternate, clefted equilibrium shape. Compared to method (i), method (ii) is computationally a more efficient clefting test. The test consists in setting up the balloon in its symmetrically inflated configuration, then breaking the symmetry of this shape by artificially introducing a clefting imperfection, and finally determining the equilibrium shape of the balloon. The clefting imperfection is computed by shifting the constraint at the bottom of the balloon and removing the pressure in the bottom region, below the shifted constraint. The clefting test is applied successfully to three 27~m diameter superpressure balloons that have been tested indoors by NASA, of which one had remained clefted when it was inflated and the other two had deployed completely. In addition to numerical simulations, formulation of a new cleft factor, employed as an indicator of tendency to S-cleft for superpressure balloons based on constant-stress design has been established through dimensional analysis. The cleft factor, defined as the ratio of clefted volume to cyclically symmetrical volume, is expressed in the form of power law relation of the dimensionless groups. An example illustrates how to calculate the coefficients of the analytical formula and analyze sensitivity of design parameters to clefting.