Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Estimating stresses in a partially inflated high altitude balloon using a relaxed energy

Author: William G. Collier Jr.
Journal: Quart. Appl. Math. 61 (2003), 17-40
MSC: Primary 74K15; Secondary 74B20, 74G65
DOI: https://doi.org/10.1090/qam/1955222
MathSciNet review: MR1955222
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Abstract: During ascent and at other times during flight, the lifting gas of a high altitude balloon is compressed and only able to partially inflate the balloon. In this condition the surface of the balloon will sag to form folds and wrinkles which are difficult to analyze. Previous numerical work to analyze these types of balloons was based on minimizing extrema of potential energy of balloon shapes that included an explicit representation of excess material as folds. These models used the conventional strain energy for linear isotropic membranes and permitted compressive states to enter the solutions. This paper explores the application of the energy relaxation method to the earlier models to produce solutions free of compressive states. Numerical results computed using the relaxed energy are presented and compared with results computed using the standard strain energy for a membrane.

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DOI: https://doi.org/10.1090/qam/1955222
Article copyright: © Copyright 2003 American Mathematical Society

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