Non-linear visco-elastic analysis and the design of super-pressure balloons : stress, strain and stability

Tensys have a long-established background in the shape generation and load analysis of architectural stressed membrane structures. Founded upon their inTENS finite element analysis suite, these activities have broadened to encompass ‘lighter than air' structures such as aerostats, hybrid air-vehicles and stratospheric balloons. Since 2004 Tensys have acted as consultants to the NASA Ultra Long Duration Balloon (ULDB) Program. Early implementations of the super-pressure balloon design chosen for ULDB have shown problems of geometric instability, characterised by improper deployment and the potential for overall geometric instability once deployed. The latter has been reproduced numerically using inTENS, and the former are better understood following a series of large-scale hangar tests simulating launch and ascent. In both cases the solution lies in minimising the film lobing between the tendons. These tendons, which span between base and apex end fittings, cause the characteristic pumpkin shape of the balloons and also provide valuable constraint against excessive film deformation. There is also the requirement to generate a biaxial stress field in order to mobilise in-plane shear stiffness. A consequence of reduced lobing between tendons is the development of higher stresses in the balloon film under pressure. The different thermal characteristics between tendons and film lead to further significant meridional stress under low temperature flight conditions. The non-linear viscoelastic response of the envelope film acts positively to help dissipate excessive stress and local concentrations. However, creep over time may produce lobe geometry variations sufficient to compromise the geometric stability of the balloon. The design of a balloon requires an analysis approach that addresses the questions of stress and stability over the duration of a flight by time stepping analyses using an appropriate material model. This paper summarises the Dynamic Relaxation approach to stress and stability analysis inherent in inTENS, and focuses in particular on: Implementation of an alternative application of the Incremental Schapery Rand (ISR) representation of the non-linear visco-elastic response of the polyethylene balloon film. This is based upon the relaxation modulus, rather than the creep compliance, and as such fits more efficiently into the Dynamic Relaxation analysis procedure used within inTENS. Comparisons of results between the two approaches are given. Verification of the material model by comparison with material tests. Verification of the application to pumpkin balloon structures by comparison with scale model tests. Application of inTENS with ISR to time-stepping analyses of a balloon flight including diurnal variations of temperature and pressure. This includes the demonstration of a method for checking the likely hood of overall instability developing at any particular time in the flight as both balloon geometry and film properties change due to visco-elastic effects.