Volume 4, Issue 3
Group Invariant Solutions of the Plastic Torsion of Rod with Variable Cross Section

Kefu Huang and Houguo Li

10.4208/aamm.10-m1201

Adv. Appl. Math. Mech., 4 (2012), pp. 382-388.

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  • Abstract

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.

  • History

Published online: 2012-04

  • AMS Subject Headings

74C05, 76M60

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