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1 results

  • Group Invariant Solutions of the Full Plastic Torsion of Rod with Arbitrary Shaped Cross Sections

  • Kefu Huang, Houguo Li
  • Journal:
    Advances in Applied Mathematics and Mechanics / Volume 4 / Issue 3 / June 2012
    Published online by Cambridge University Press:
    03 June 2015, pp. 382-388
    Print publication:
    June 2012

  • Based on the theory of Lie group analysis, the full plastic torsion of rod with arbitrary shaped cross sections that consists in the equilibrium equation and the non-linear Saint Venant-Mises yield criterion is studied. Full symmetry group admitted by the equilibrium equation and the yield criterion is a finitely generated Lie group with ten parameters. Several subgroups of the full symmetry group are used to generate invariants and group invariant solutions. Moreover, physical explanations of each group invariant solution are discussed by all appropriate transformations. The methodology and solution techniques used belong to the analytical realm.