Abstract
This paper presents results obtained from numerical simulations of the responses of an elastic-plastic thin cylindrical shell to fluctuating axisymmetric temperature in the presence of uniform axial stresses. The engineering situation considered has practical importance in nuclear reactors and has been the subject of a number of earlier studies. The main purpose is to assess quantitatively the influence of geometry changes, primarily due to plastic yielding, on shakedown and ratchetting (incremental collapse) phenomena. In particular, these phenomena are investigated with respect to both the stabilizing effects of tensile primary stresses on them, and their strong interference with elastoplastic buckling. The systematic evolutive analyses presented herein are also intended to critically assess the validity of earlier results (mainly condensed in the socalled Brussels diagrams) which have been established by simplified methods of shakedown based on the small deformation (no geometric effects) hypothesis.
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References
1987 KÖnig, J.A., Shakedown of elastic-plastic structures, Elsevier, Amsterdam.
1981 KÖnig, J.A. and Maier, G., “Shakedown analysis of elastoplastic structures: a review of recent developments”, Nuclear Engng Design, 66, pp. 81–95.
1979 Cohn, M.Z., and Maier, G., Engineering plasticity by mathematical programming, Pergamon, New York.
1981 Zyczkowski, M., Combined loadings in the theory of plasticity, PWN, Pol. Sci. Publ., Warsaw.
1989 Kaliszky, S., Plasticity: theory and engineering applications, Elsevier, Amsterdam.
1972 Maier, G., “A shakedown matrix theory allowing for workhardening and second-order geometric effects”, in: Foundations of plasticity, Vol. I (A. Sawczuk, Ed.), Noordhoff, Leyden, pp. 417–433.
1973 Maier, G., “Upper bounds on deformations of elastic work-hardening structures in the presence of dynamic and second order effects”, J. Struct. Mech., 2.(4), pp. 265–280.
1976 KÖnig, J.A. and Maier, G., “Adaptation of rigid-work-hardening discrete structures subjected to load and temperature cycles and second-order geometric effects”, Comput. Meth. Appl. Mech. Engng, 8, pp. 37–50.
1990 Maier, G. and Novati, G., “A shakedown and bounding theory allowing for nonlinear hardening and second-order geometric effects with reference to discrete structural models”, in: Inelastic solids and structures, A. Sawczuk Memorial Volume (M. Kleiber and J.A. König, Eds) Pineridge, Swansea, pp. 451–471.
1984 KÖnig, J.A., “Stability of the incremental collapse” in: Inelastic structures under variable loads, (C. Polizotto and A. SwaczukEds), COGRAS, Palermo, pp. 329–334.
1988 KÖnig, J.A. and Siemaszko, A., “Strain hardening effects in shakedown processes”, Ing. Archiv., 58, pp. 58–66.
1985 Siemaszko, A. and KÖnig, J.A., “An analysis of stability of incremental collapse of skeletal structures”, J. Struct. Mech., 13, pp. 301–321.
1990 Siemaszko, A. and KÖnig, J.A., “Geometric effects in shakedown of optimum structures”, in: Inelastic solids and structures, A. Sawczuk Memorial Volume, (M. Kleiber and J.A. König, Eds) Pineridge, Swansea, pp. 503–515.
1989 Texeira De Freitas, J.A. and Smith, D.L. “The post-collapse behaviour of rigid-plastic structures”, Eur. J. Mech. A/Mech. A/Solid, 1, pp. 35–52.
1983 Weichert, D., “Shakedown at finite displacement; a note on Melan's theorem”, Mech. Res. Comm., Ü pp. 121–127.
1986 Weichert, D., “On the influence of geometrical nonlinearities on the shakedown of elastic-plastic structures”, Int. J. Plasticity, 2, 135–148.
1986 Weichert, D., “Elastic-plastic structures under variable loads at small strain and moderate rotations”, in: Finite Rotations in Structural Mechanics, (W. Pietraszkiewicz, Ed.), Springer, Berlin, pp. 343–356.
1990 Weichert, D., “Advances in the geometrically nonlinear shakedown theory”, in: Inelastic solid and structures, A. Swaczuk Memorial Volume, (M. Kleiber and J.A. König, Eds) Pineridge, Swansea, pp. 489–502.
1990 Gross-Weege, J., “A unified formulation of statical shakedown criteria for geometrically nonlinear problems”, Int. J. Plasticity, 6, pp. 433–477.
STUMPF, H., “Theoretical and computational aspects in the shakedown analysis of finite elastoplasticity”, Int. J. Plasticity, (To appear).
1983 Nguyen Quoc Son and Gary, G. “Flambage par deformations plastiques cumulées sous charge cyclique additionnelle”, J. de Méc. Théorique Appl., 3, pp. 351–373.
1991 Pycko, S. and KÖnig, J.A., “Steady plastic cycles on reference configuration in the presence of second-order geometric effects”, J. Mech. A/Solids, 10, pp. 563–574.
1982 Polizzotto, C, “ A unified treatment of shakedown theory and related boundary techniques”, Solid Mech. Arch., 1, pp 19–75.
1985 Ponter A.R.S. and Karadeniz, S., “An extended shakedown theory for structures that suffer cyclic thermal loading, part 1: theory”, J. AppL Mech., 52, pp. 877–882.
1990 Ponter, A.R.S. and Karadeniz, S., “An extended shakedown theory for structures that suffer cyclic thermal loading, part 2: applications”, J. Appl. Mech., 52, pp. 883–889.
1990 Stein, E., Zhang, G., Mahnken, R. and KÖnig, J.A., “Micromechanical modelling and computation of shakedown with nonlinear kinematic hardening including examples for 2-D problems”, Proc. of CSME, Mech. Eng. Forum., Toronto, pp. 425–430.
1985 Leers, K., Klie W., KÖnig, J.A. and Mahrenholtz, O. “Experimental investigations on shakedown of tubes”, Plasticity Today, (A. Sawczuk and G. Bianchi, Eds), Elsevier, London, pp. 259–275.
1987 Karadeniz, S. Ponter, A.R.S. and Carter, K.F., “The plastic ratchetting of thin cylindrical shells subjected to axisymmetric thermal and mechanical loading”, ASME J. Press. Vessel Tech., 109, pp. 387–393.
1991 Save, M, DesaxcÉ, G. and Borkowski, A. “Computation of shakedown loads: feasibility study”, CEC Dir. Gen. Science, Res. and Dev., Nuclear Sci. and Techn., Report EUR13618EN., Brussels.
1967 Bree, J. “Elastoplastic behaviour of thin tubes subjected to internal pressure and intermittent high heat fluxes with application to fast nuclear reactor fuel elements”, J. Strain Analysis, 2, pp. 226–238.
1985 Cocks, A.C.F. and Ponter, A.R.S., “The plastic behaviour of components subjected to constant primary stresses and cyclic secondary strains”, J. Strain Analysis, 20(l), pp. 7–14.
1991 Hibbitt, Karlsson and Sorensen, “ABAQUS, Version 4.9”, Providence, RI.
1991 Bazant, Z.P. and Cedolin, L., Stability of structures, Oxford University Press, Oxford.
1983 Calladine, Cr., Theory of shell structures, Cambridge University Press, London.
1991 Pignataro, M., Rizzi, N. and Luongo, A, Stability, bifurcation and poscritical behaviour of elastic structures, Elsevier, Amsterdam.
1972 Hutchinson, J.W., “On the postbuckling behaviour of imperfection-sensitive structures in the plastic range”, J. Appl. Mech., 39, pp. 155–162.
1991 Shen, H.S. and Chen, T.Y., “Buckling and postbuckling behaviour of cylindrical shells under combined external pressure and axial compression”, Thin-walled Structures, 12, pp. 321–334.
1983 ECCS, “European Recommendations for Steel Construction: Buckling of Shells”, CCCS PubL, N° 29, Brussels.
1990 Galletly, G.D. and Blachut, J., “Axially-compressed cylindrical shells: a comparison of experiment and theory” in: Inelastic Solid and Structures, A. Sawczuk Memorial Volume, (M. Kleiber and J.A. König, Eds) Pineridge, Swansea, pp. 257–276.
1992 Teng, J. and Rotter, J.M. “Buckling of pressurized axi symmetrically imperfect cylinders under axial loads”, J. eng. Mech. ASCE, 118. pp. 229–247.
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Maier, G., Pan, L.G., Perego, U. (1995). Geometric Effects on Shakedown and Ratchetting of Axisymmetric Cylindrical Shells Subjected to Variable Thermal Loading. In: Mróz, Z., Weichert, D., Dorosz, S. (eds) Inelastic Behaviour of Structures under Variable Loads. Solid Mechanics and Its Applications, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0271-1_13
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