Group Invariant Solutions of the Plastic Torsion of Rod with Variable Cross Section (Advances in Applied Mathematics and Mechanics, 2012)
Based on the theory of Lie group analysis, the full plastic torsion of rodwith arbitrary shaped cross sections that consists in the equilibrium equation andthe non-linear Saint Venant-Mises yield criterion is studied. Full symmetry groupadmitted by the equilibrium equation and the yield criterion is a finitely generatedLie group with ten parameters. Several subgroups of the full symmetry groupare used to generate invariants and group invariant solutions. Moreover, physicalexplanations of each group invariant solution are discussed by all appropriatetransformations. The methodology and solution techniques used belong to the analyticalrealm.