Abstract
The considered membrane shell is held together against the gas pressure due to tensile forces within the walls. The optimization problems consist in search of the shape and the thickness distribution of membrane shells. The shape of the shell and the thickness are unknowns. The exact closed form solution for the optimal shape is obtained and corresponding isoperimetric inequality is stated for a reasonably broad type of stress criteria. From the viewpoint of the demonstrated isoperimetric inequality the non-sphericity of the optimal pressure vessels reported in the articles (Banichuk in Mech Dokl Phys 50(11):605–609, 2005. doi:10.1134/1.2137798; Banichuk et al. in Meccanica 40(2):135–145, 2005; Struct Multidiscipl Optim 35:453–459, 2008. doi:10.1007/s00158-007-0149-8; Timonin in Mech Solids MTT 3:183–185, 1984) is explained.
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Kobelev, V. The lightest pressure vessel. Meccanica 52, 483–486 (2017). https://doi.org/10.1007/s11012-016-0415-1
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DOI: https://doi.org/10.1007/s11012-016-0415-1