A method for calculating the ultimate true stresses arising in the walls of shells of revolution in the area of uniform plastic deformation is developed in the research. In order to derive the stability loss for the plastic deformation process the criterion of maximum load is taken as the basis, simple differential equations were solved. It has been shown analytically that the level of the boundary true stresses is much lower when the values of the principal stress ratios approach to 2 or 1/2 compared to the adjacent stress states.
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 Tomita, Y., Shindo, A., Nagai, M. “Axisymmetric deformation of circular elastic-plastic tubes under axial tension and internal pressure”, International Journal of Mechanical Sciences 26, pp. 437 - 444, 1984. DOI: 10.1016/0020-7403(84)90033-X
 Shahabi, M., Esmaeilnejad, M., Ghasemi, A. “A thin-walled tube subjected to combined internal pressure and axial load under different loading paths”, Strojnícky časopis – Journal of Mechanical Engineering 63 (5-6), p. 307, 2012.
 Chmelko, V., Krššák, P. “The elasto-plastic state solution of a heavy-wall cylindrical pressure vessel using bilinear stress-strain model. Part 1: Derivation of analytical relations”, Strojnícky časopis – Journal of Mechanical Engineering 64 (1), p. 51, 2013.
 Bazhenov, V. G., Lomunov, V. K. “An experimental-theoretical study of the process of neck formation under tension of a steel tubular specimen before rupture”, In: Problems of durability and plasticity, Publishing House of the UNN, Nizhny Novgorod, Russia, pp. 35 – 41, 2001.
 Grigolyuk, E. I., Kabanov, V., “Stability of shells”, Science, Moskow, USSR, 1978.
 Middleton, J., Owen, DRJ., “Automated design optimization to minimize shearing stress in axisymmetric pressure-vessels”, Nuclear Engineering and Design 44 (3), pp. 357 - 366, 1977.
 Błachut, J. “Minimum weight of internally pressurised domes subject to plastic load failure”, Thin-Walled Structures 27(2), pp. 127 – 146, 1997. DOI:10.1016/s0263-8231(96)00036-5
 Zhu, L., Boyle, J.T., “Optimal shapes for axisymmetric pressure vessels: a brief overview”, Journal of Pressure Vessel Technology-transactions of the ASME 122 (4), p. 443, 2000. DOI:10.1115/1.1308572
 Carbonari, R. C., Muñoz-Rojas, P. A., Andrade, E. Q., Paulino, G. H., Nishimoto, K., Silva, E. C. N. “Design of pressure vessels using shape optimization: An integrated approach”, International Journal of Pressure Vessels and Piping 88 (5-7), pp. 198 – 212, 2011. DOI: 10.1016/j.ijpvp.2011.05.005
 Nadai, A. “Plasticity and destruction of solids”, Volume 1, ed. Shapiro, G. S., in 2 volumes, Foreign Literature, Moscow, USSR, 1954.
 “Soprotivlenie materialov [Strength of Materials]”, In: Book editor with. Smirnov, A.F., Vysshaya shkola, Moskow, 1975.
 Lebedev, A.A., Kovalchuk, B.I., Giginyak, F.G., Lamashevsky, V.P. “Mechanical Properties of Structural Materials under Complex Stress”, In: Book editor with Lebedev, A.A., In Yure, Kyiv, Ukraine, 2003. ISBN 966-8088-36-0
 Friedman, Ya. B. “Mechanical properties of metals”, All-Union order of Lenin scientific research institute of aviation materials, Oborongiz, Moskow, 1946.
 Robert, H. “Mathematical theory of plasticity” ed. trans. Grigolyuk, E. I., Gostekhizdat, Moscow, 1956.
 Kaminsky, A.A., Bastun, V.N. “Deformation hardening and fracture of metals at variable loading processes”, Scientific Thought, Kyiv, 1985.
 Shkodzinsky, O.K., Kozbur, G.V. “Investigation of the stability of the process of plastic deformation of a thin-walled tube under conditions of complex stress state”, Bulletin of the TDTU 14 (3), pp. 24 – 31, 2009.
 Giginyak, F.F., Lebedev, A.A., Shkodzinsky, O.K. “Strength of structural materials at low cycle load under conditions of complex stress state”, Scientific Thought, Kyiv, 2003. ISBN 9660007868