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

Published online by Cambridge University Press:  03 June 2015

Kefu Huang  and
Houguo Li
Kefu Huang*
Affiliation:
Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
Houguo Li*
Affiliation:
Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
*
URL:http://en.coe.pku.edu.cn/faculty/faculty, Email: huangkefu@coe.pku.edu.cn
Corresponding author. Email: aodingfulie@gmail.com
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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.

Keywords

74C0576M60Lie group analysisgroup invariant solutionfull plastic torsionyield criterion
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 3 , June 2012 , pp. 382 - 388
Copyright
Copyright © Global-Science Press 2012

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