Computational Methods for Membrane Structures

Markus Pagitz

Abstract

<>Balloon technology has steadily improved since the first flight by the Montgolfier brothers in 1783. Nowadays the focus of development is to create helium filled balloons that can stay at a height between 30 and 50 km for up to 100 days carrying a payload of several tonnes. This kind of balloons will be used to create platforms for telecommunication, intelligence or atmospheric research. The most advanced program in developing this new generation of balloons is the ULDB Ultra Long Duration Balloon from NASA.
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These balloons have not much in common with the first small gas balloons developed by Charles as their dimensions are with diameters of more than one hundred meters - enormous. Furthermore the structure itself is quite different from the first approaches. An ULDB is made of a large number of lobes with reinforcing tendons at their seams that meet at the top and bottom apexes. The advantage of a lobed balloon is that the membrane between two tendons has a higher curvature than the overall shape of the balloon wherefore the pressure forces can be carried more efficiently to the meridional tendons by the membrane. Due to the similarity between pumpkins and ULDB's the latter are often called pumpkin balloons. One of the problems that occurred during the ascent of several pumpkin shaped balloons in the atmosphere was that they did not deploy into the desired shape. The study of this phenomenon is the goal of this thesis.
<>In order to build up numerical models which are able to simulate the instability of balloons it is essential to develop the necessary computational tools. As balloons are made out of very thin membranes, and therefore susceptible to wrinkles, the first part of this thesis deals with a novel finite element that can be used for the simulation of wrinkled membranes. One of the properties of this new element is that it can be used for heavily wrinkled structures without the necessity of changing the material or deformation tensor at every iteration step. The performance of this element is verified by showing that it correctly represents the shearing of a thin rectangular membrane, the bending of an inflated membrane cylinder with end loads, and the form finding of catenoids and isotensoids.

The second part of this thesis looks at the stability of simple lobed balloon structures. The structures under investigation are a single truncated isotensoid and a stack of four truncated isotensoids forming a kind of lobed cylinder. This lobed cylinder is an axi-symmetric, idealised version of the lobed pumpkin balloons that have occasionally deployed into anomalous, clefted configurations. By studying these simplified structures it is possible to draw some preliminary conclusions about general features of the behaviour of lobed pumpkin balloons.

Key words: non-linear finite element, wrinkled membrane, isotensoid, balloons, stability

[Cambridge University | CUED | Structures Group | Geotechnical Group]

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