TY - JOUR
T1 - Group Invariant Solutions of the Plastic Torsion of Rod with Variable Cross Section
AU - Huang , Kefu
AU - Li , Houguo
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 382
EP - 388
PY - 2012
DA - 2012/04
SN - 4
DO - http://doi.org/10.4208/aamm.10-m1201
UR - https://global-sci.org/intro/article_detail/aamm/126.html
KW - Lie group analysis, group invariant solution, full plastic torsion, yield criterion.
AB - <p style="text-align: justify;">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.</p>