This paper derives the minimum-weight shapes of head closures for cylindrical pressure vessels. Head configurations, weights, and membrane stresses are obtained for thin-shell heads of isotropic materials with uniform internal pressure by restricting the knuckle shear stresses to constant values where possible and by minimizing the weight of prescribed-shape heads. Torispherical, ellipsoidal, and Biezeno-type heads with constant and varying thickness (neglecting the effects of bending) are investigated. Enclosed-volume constancy and supporting structures are also considered. Certain highly efficient shapes are obtained that weigh up to 11 per cent less than the corresponding hemispherical capping closure.
Minimum-Weight Proportions of Pressure-Vessel Heads
G. A. Hoffman
Aero-Astronautics Department, The RAND Corporation, Santa Monica, Calif.
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Hoffman, G. A. (December 1, 1962). "Minimum-Weight Proportions of Pressure-Vessel Heads." ASME. J. Appl. Mech. December 1962; 29(4): 662–668. https://doi.org/10.1115/1.3640651
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