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Application of Lie Group Analysis to the Plastic Torsion of Rod with the Saint Venant–Mises Yield Criterion

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Abstract:

Based on Lie group and Lie algebra theory, the basic principles of Lie group analysis of differential equations in mechanics are analyzed, and its validity in theory of plasticity is explained by example. For the plastic torsion of rod with variable cross section that consists in non-linear Saint Venant-Mises yield criterion, the 10-dimensional Lie algebra admitted by the equilibrium equation and yield criterion is completely solved, and invariants and group invariant solutions relative to different sub-algebras are given. At last, physical explanations of each group invariant solution are discussed by some types of transformations.

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Periodical:

Advanced Materials Research (Volume 461)

Pages:

265-271

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.461.265

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Online since:

February 2012

Authors:

Hou Guo Li

Keywords:

Group Invariant Solutions, Lie Group Analysis, Plastic Torsion, Saint Venant–Mises Yield Criterion

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© 2012 Trans Tech Publications Ltd. All Rights Reserved

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References

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