A numerical method for the analysis of the stress–strain state and strength of a thin-walled structural member subject to increasing internal pressure is proposed. It is based on the constitutive equations describing the elastoplastic deformation of isotropic materials along small-curvature paths and taking into account the stress mode, the theory of thin shells of revolution, failure criterion, and a method to solve a boundary-value problem of plasticity. Numerical values of the critical load are found
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M. E. Babeshko, Yu. N. Shevchenko, and N. N. Tormakhov, “Thermoviscoplasticity theory incorporating the third deviatoric stress invariant,” Int. Appl. Mech., 51, No. 1, 85–91 (2015).
L. M. Kachanov, Fundamentals of the Theory of Plasticity, Dover, New York (2004).
V. V. Novozhilov, Thin Shell Theory, Noordhoff, Groningen (1964).
V. P. Sdobyrev, ”Long-term strength of EI 437B alloy in combined stress state,” Izv. AN SSSR, OTN, No. 4, 92–97 (1958).
Yu. N. Shevchenko, M. E. Babeshko, and R. G. Terekhov, Thermoviscoelastoplastic Processes of Combined Deformation of Structural Members [in Russian], Naukova Dumka, Kyiv (1992).
M. E. Babeshko and Yu. N. Shevchenko, ”Describing the thermoelastoplastic deformation of compound shells under axisymmetric loading with allowance for the third invariant of stress deviator,” Int. Appl. Mech., 46, No. 12, 1362–1371 (2010).
M. E. Babeshko, Yu. N. Shevchenko, and N. N. Tormakhov, ”Approximate description of the inelastic deformation of an isotropic material with allowance for the stress mode,” Int. Appl. Mech., 46, No. 2, 139–148 (2010).
M. E. Babeshko and Yu. N. Shevchenko, ”Studying the axisymmetric thermoviscoelastoplastic deformation of layered shells taking into account the third deviatoric stress invariant,” Int. Appl. Mech., 50, No. 6, 615–626 (2014).
D. C. Drucker and R. T. Shield, “Limit analysis of symmetrically loaded shells of revolution,” J. Appl. Mech., 25, 61–68 (1959).
G. D. Galletly and J. Blachut, “Torispherical shells under internal pressure-failure due to asymmetric plastic buckling of axisymmetric yielding,” Proc. Inst. Mech. Engineers, 119, 225–238 (1985).
G. D. Galletly and S. K. Radhamohan, ”Elastic-plastic buckling of internally pressurized thin torispherical shells,” J. Press. Vess. Tech., 101, 216–225 (1979).
A. Z. Galishin and Yu. N. Shevchenko, ”Determining the axisymmetric thermoelastoplastic state of thin shells with allowance for the third invariant of the deviatoric stress tensor,” Int. Appl. Mech., 49, No. 6, 675–684 (2013).
S. K. Radhamohan and G. D. Galletly, ”Plastic collapse of thin internally pressurized torispherical shells,” J. Press. Vess. Tech., 101, 311–320 (1979).
Yu. N. Shevchenko, R. G. Terekhov, and N. N. Tormakhov, ”Constitutive equations for describing the elastoplastic deformation of elements of a body along small-curvature paths in view of the stress mode,” Int. Appl. Mech., 42, No. 4, 421–430 (2006).
Yu. N. Shevchenko and N. N. Tormakhov, ”Thermoviscoplastic deformation along paths of small curvature: Constitutive equations including the third deviatoric stress invariant,” Int. Appl. Mech., 48, No. 6, 688–699 (2012).
R. T. Shield and D. C. Drucker, “Design of thin-walled tori-conical pressure-vessel heads,” J. Appl. Mech., 83, 292–297 (1961).
J. Soric, ”Stability analysis of a torispherical shell subjected to internal pressure,” Comp. & Struct., 36, 147–156 (1990).
J. Soric, ”Geomtrisch nichtlineare berechnung torispharischer schalen unter innendruck,” Stahlbau, 59, 269–274 (1990).
J. Soric and W. Zahlten, ”Elastic-plastic analysis of internally pressurized torispherical shells,” Thin-Walled Structures, 22, 217–239 (1995).
A. Zolochevsky, ”Creep of isotropic and anisotropic materials with different behavior in tension and compression,” in: M. Zyczkowski (ed.), Creep in Structures, Springer-Verlag, Berlin (1991), pp. 217–220.
A. Zolochevsky, A. Z. Galishin, S. Sklepus, and G. Z. Voyiadjis, ”Analysis of creep deformation and creep damage in thin-walled branched shells from materials with different behavior in tension and compression,” J. Solids Struct., 44, No. 16, 5075–5100 (2007).
A. Zolochevsky, S. Sklepus, T. H. Hyde, A. A. Becker, and S. Paravali, ”Numerical modeling of creep and creep damage in thin plates of arbitrary shape from materials with different behavior in tension and compression under plane stress conditions,” Int. J. Numer. Meth. Eng., 80, No. 11, 1406–1436 (2009).
M. Zyczkowski, Combined Loadings in the Theory of Plasticity, Polish Sci. Publ., Warsaw (1981).
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Translated from Prikladnaya Mekhanika, Vol. 51, No. 3, pp. 86–94, May–June 2015.
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Babeshko, M.E., Galishin, A.Z., Semenets, A.I. et al. Influence of the Stress Mode on the Strength of High-Pressure Vessels. Int Appl Mech 51, 319–325 (2015). https://doi.org/10.1007/s10778-015-0692-8
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DOI: https://doi.org/10.1007/s10778-015-0692-8