Structural Engineering and Mechanics

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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)
  • Received : 2002.10.12
  • Accepted : 2003.06.14
  • Published : 2003.08.25
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Abstract

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.

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References

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