Summary
Plastic collapse modes of a thick-walled homogeneous cylinder under circularly-symmetrical loading (internal and external normal pressures) are analyzed. Ideal plasticity,Huber-Mises-Hencky yield condition, incompressibility and plane strain conditions are assumed. The possibility of existence of non-symmetrical plastic collapse modes corresponding to circularly-symmetrical stress distribution is found. General non-symmetrical solution is presented in the form ofFourier series and illustrated by some numerical examples.
Zusammenfassung
Die Figuren des plastischen Kollapses eines dickwandigen homogenen Zylinders unter drehsymmetrischer Belastung (innerer und äußerer Druck) werden analysiert. Ideale Plastizität,Huber-Mises-Henckysche Fließbedingung, Inkompressibilität und ebener Verzerrungszustand werden angenommen. Die Möglichkeit nicht symmetrischer Kollapsfiguren bei drehsymmetrischer Spannungsverteilung wird aufgezeigt. Die allgemeine nicht symmetrische Lösung wird alsFourierreihe angegeben und durch einige numerische Beispiele illustriert.
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References
Belayev, N. M. andA. K. Sinitsky: Napryazhenje i deformacij v tolstostennykh cilindrakh pri uprugo-plasticheskom sostoyanii materiala. (Stresses and strains in thick-walled cylinders in elastic-plastic range, in Russian). Izv. AN SSSR, Otd. Tekhn. Nauk2, 3–54 (1938).
Hill, R., E. H. Lee, andS. J. Tupper: The theory of combined plastic and elastic deformation with particular reference to a thick tube under internal pressure. Proc. Roy. Soc. (A),191, 278–303 (1947).
Hill, R.: The mathematical theory of plasticity. Oxford 1950. At the Clarendon Press.
Hill, R.: On the problem of uniqueness in the theory of a rigid-plastic solid. J. Mech. Phys. Solids4, 4 247–255 (1956);5, 1 1–8 (1956).
Hodge, P. G., Jr., andG. N. White, Jr.: A quantitative comparison of flow and deformation theories of plasticity. J. Appl. Mech.17, 180–184 (1950).
Panarelli, E. J. andP. G. Hodge Jr.: Interaction of pressure, end load, and twisting moment for a rigid-plastic circular tube. Trans. ASME,E 30, 3, 396 to 400 (1963).
Rozenblyum, V. I.: O plasticheskikh raschetakh tolstostennykh cilindrov. (On the calculation of plastic thick-walled tubes, in Russian). Inzh. Zhurnal, Mekh. Tverd. Tela,4, 133–137 (1966).
Rychlewski, J.: O korrektnosti resheniy zadach idealnoy plastichnosti. (On the correctness of the solutions of ideal plasticity, in Russian). Bull. Acad. Polon. Sci., Serie Sci. Techn.11, 225–232 (321–328) (1963).
de Saint-Venant, B.: Compt. Rend.74, 1009 (1872).
Skrzypek, J. andM. Życzkowski: Limit state of a thick-walled tube under simultaneous torsion, tension and pressure gradient. Bull. Acad. Polon. Sci., Serie Sci. Techn.13, 285–294 (1965).
Skrzypek, J.: Dolne oszacowanie nośności granicznej nierozciagliwego grubościennego rurociagu. (Lower bound solution for limit carrying capacity of an inextensible thick-walled pipe-line, in Polish). Archiwum Budowy Maszyn16, 1 (1969).
Turner, L. B.: Trans. Camb. Phil. Soc.21, 377 (1909).
Życzkowski, M.: The limit load of a thick-walled tube in a general circularly-symmetrical case. Arch. Mech. Stos.8, 155–179 (1956).
Życzkowski, M.: Certain general equations for plane circularly symmetrical plastic states. Arch. Mech. Stos.10, 463–478 (1958).
Życzkowski, M.: Combined loadings in the theory of plasticity. Int. J. Non-Linear Mechanics2, 173–205 (1967).
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Skrzypek, J., Życzkowski, M. Non-symmetrical plastic collapse modes of a symmetrically loaded circular cylinder. Acta Mechanica 7, 213–223 (1969). https://doi.org/10.1007/BF01176669
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DOI: https://doi.org/10.1007/BF01176669