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

Kefu Huang & Houguo Li

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

Published online: 2012-04

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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.

  • AMS Subject Headings

74C05, 76M60

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COPYRIGHT: © Global Science Press

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@Article{AAMM-4-382, author = {Huang , Kefu and Li , Houguo}, title = {Group Invariant Solutions of the Plastic Torsion of Rod with Variable Cross Section}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {3}, pages = {382--388}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1201}, url = {http://global-sci.org/intro/article_detail/aamm/126.html} }
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 -

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.

Kefu Huang & Houguo Li. (1970). Group Invariant Solutions of the Plastic Torsion of Rod with Variable Cross Section. Advances in Applied Mathematics and Mechanics. 4 (3). 382-388. doi:10.4208/aamm.10-m1201
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