Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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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  • [AS98] A. A. Atai and D. J. Steigmann, Coupled deformations of elastic curves and surfaces, Int. J. Solids Structures 35(16), 1915-1952 (1998) MR 1615737
  • [Bag96] F. Baginski, Modeling nonaxisymmetric off-design shapes of large scientific balloons, AIAA Journal 34(2), 400-407 (1996)
  • [BB98] F. Baginski and K. A. Brakke, Modeling ascent configurations of strained high altitude balloons, AIAA Journal 36(10), 1901-1910 (1998)
  • [BC98] F. Baginski and W. Collier, A mathematical model for the strained shape of a large scientific balloon at float altitude. Manuscript, George Washington University, 1988, J. Appl. Mech., Vol. 67, issue 1, pp. 6-16, 2000
  • [BR95] F. Baginski and S. Ramamurti, Variational principles for ascent shapes of large scientific balloons, AIAA Journal 33(4) 764-768 (1995)
  • [Cia88] P. Ciarlet, Mathematical Elasticity. Vol. 1, Elsevier Science Publishers, Amsterdam, 1988
  • [Dac89] B. Dacorogna, Direct Methods in the Calculus of Variations, Springer-Verlag, 1989 MR 990890
  • [Fis88] D. Fisher, Configuration dependent pressure potentials, Journal of Elasticity 19, 77-84, 1988 MR 928728
  • [HS94] E. M. Haseganu and D. J. Steigmann, Analysis of partly wrinkled membranes by the method of dynamic relaxation, Computational Mechanics 14, 596-614 (1994) MR 1297647
  • [Pip86] A. C. Pipkin, The relaxed energy density for isotropic elastic membranes, IMA Journal of Applied Mathematics 36, 85-99 (1986) MR 984460
  • [Pip94] A. C. Pipkin, Relaxed energy densities for large deformations of membranes, IMA Journal of Applied Mathematics 52, 297-308 (1994) MR 1281300
  • [Sch91] W. W. Schur, Structural behavior of scientific balloons; finite element simulation and verification, 1991. AIAA-91-3668-CP
  • [Sch97] W. W. Schur, Structural response of a zero-pressure balloon with an axial load tendon. In AIAA International Balloon Technology Conference. AIAA, June 1997
  • [Sou94] A. Soubrier, French contribution to new balloon designs and materials. Adv. Space Res. 14(2), (2)5-(2)12 (1994)
  • [Ste91a] D. J. Steigmann, A note on pressure potentials, Journal of Elasticity 26, 87-93 (1991) MR 1128932
  • [Ste91b] D. J. Steigmann, Tension-field theories of elastic membranes and networks, AMD 124, 41-49 (1991)

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Additional Information

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

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