Structural Engineering and Mechanics

  • 제16권2호
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  • Pages.141-152
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  • 2003
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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Characteristics of solutions in softening plasticity and path criterion

  • Chen, G. (Faculty of Engineering & Surveying, The University of Southern Queensland) ;
  • Baker, G. (Faculty of Engineering & Surveying, The University of Southern Queensland)
  • 투고 : 2002.10.12
  • 심사 : 2003.06.14
  • 발행 : 2003.08.25
⟨ 이전 논문 다음 논문 ⟩

초록

Characteristics of solutions of softening plasticity are discussed in this article. The localized and non-localized solutions are obtained for a three-bar truss and their stability is evaluated with the aid of the second-order work. Beyond the bifurcation point, the single stable loading path splits into several post-bifurcation paths and the second-order work exhibits several competing minima. Among the multiple post-bifurcation equilibrium states, the localized solutions correspond to the minimum points of the second-order work, while the non-localized solutions correspond to the saddles and local maximum points. To determine the real post-bifurcation path, it is proposed that the structure should follow the path corresponding to the absolute minimum point of the second-order work. The proposal is further proved equivalent to Bazant's path criterion derived on a thermodynamics basis.

키워드

참고문헌

  1. Bazant, Z.P. (1988), "Stable states and paths of structures with plasticity or damage", J. Engng. Mech., 114(12),2013-2033. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:12(2013)
  2. Bazant, Z.P. (1989), "Stable states and stable paths of propagation of damage zones and interactive fractures", InCracking and Damage: Strain Localization and Size Effect, Mazars, J. and Banzant, Z.P.(ed.) Elsevier Appl.Sci. London, 183-207.
  3. Bazant, Z.P. and Cedolin, L. (1991), Stability of Structures: Elastic, Inelastic, Fracture, and Damage Theories,Oxford University press, Oxford, New York.
  4. Chen, G. and Baker, G. (2003a), "An energy model for bifurcation analysis of a double-notched concrete panel:Simplified model", Advances in Structural Engineering, 6(1), 37-44. https://doi.org/10.1260/136943303321625711
  5. Chen, G. and Baker, G. (2003b), "An energy model for bifurcation analysis of a double-notched concrete panel:Continuous model", Advances in Structural Engineering, 6(1), 45-51. https://doi.org/10.1260/136943303321625720
  6. Chen, G. and Baker, G. (2003c), "Material stability and structural stability", Advances in Structural Engineering,in press.
  7. Goto, Y., Toba, Y. and Matsuoka, H. (1995), "Localization of plastic buckling patterns under cyclic loading", J.Engng. Mech., 121, 493-501. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:4(493)
  8. Hill, R. (1950), Mathematical Theory of Plasticity, Oxford University press, Oxford, New York.
  9. Horii, H. (1993), "Micromechanics and localization in concrete and rock", In Damage of Concrete and Rock (ed.Rossmanith, H.P.) E&FN Spon, London, 54-65.
  10. Horii, H. and Inoue, J. (1997), "New directions: Analysis of cracking localization and ultimate strength ofstructures in civil engineering", Proc. the Ninth Int. Conf. on Fracture, Sydney, Australia, 2127-2134.
  11. Hunt, G.W. and Baker, G. (1995), "Principles of localization in the fracture of quasi-brittle structures", J. Mechs.Phys. Solids, 43, 1127-1150. https://doi.org/10.1016/0022-5096(95)00028-H
  12. Hunt, G.W., Bolt, H.M. and Thompsom, J.M.T. (1989), "Structural localization phenomena and the dynamicalphase-space analogy", Proc. R. Soc. Lond, A425, 245-267.
  13. Maier, G. (1971), "On structural instability due to strain-softening", IUTAM Symposium on Instability ofContinuous Systems, Springer Verlag, Berlin, Germany.
  14. Maier, G., Zavelani, A. and Dotreppe, J.-C. (1973), "Equilibrium branching due to flexural softening", J. Eng.Mech., 99(EM4), 897-901.
  15. Needleman, A. (1972), "A numerical study of necking in circular cylindrical bars", J. Mech. Phys. Solids, 20,111-127. https://doi.org/10.1016/0022-5096(72)90035-X
  16. Needleman, A. and Tvergaard, V. (1992), "Analyses of plastic flow localization in metal", Appl. Mech. Rev., 45,Part 2, S3-S18. https://doi.org/10.1115/1.3119743
  17. Petryk, H. and Thermann, K. (1992), "On discretized plasticity problems with bifurcations", Int. J. SolidsStruct., 29, 745-765. https://doi.org/10.1016/0020-7683(92)90125-D
  18. Rice, J.R. (1976), "The localization of plastic deformation", In Theoretical and Applied Mechanics, Koiter, W.T.(ed.), North-Holland, Amsterdam, 207-220.
  19. Runesson, K., Larsson, L. and Sture, S. (1989), "Characteristics and computational procedure in softeningplasticity", J. Engng. Mech., 115, 1628-1645. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:8(1628)
  20. Stavroulakis, G.E. and Mistakidis, E.S. (1995), "Numerical treatment of hemivariational inequalities inmechanics: Two methods based on the solution of convex subproblems", Comput. Mech., 16(6), 406-416. https://doi.org/10.1007/BF00370562
  21. Tvergaard, V. and Needleman, A. (1980), "On the localization of buckle patterns, J. Appl. Mech., ASME, 21,613-619.