Chin. Phys. Lett.  2012, Vol. 29 Issue (8): 084601    DOI: 10.1088/0256-307X/29/8/084601
FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
Group Invariant Solutions of the Two-Dimensional Elastodynamics Problem in the Polar Coordinate System
LI Hou-Guo, HUANG Ke-Fu**
Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871
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Abstract Some group invariant solutions of the two-dimensional elastodynamics problem in linear homogeneous isotropic materials are considered using the group-theoretical method. In the polar coordinate system, three group invariant solutions are constructed by the invariants of the Lie group, which are admitted by the governing equations for the two-dimensional elastodynamics problem. The graphical figures of the group invariant solutions are presented, and the physical meanings of the group invariant solutions are expounded in some cases.
Received: 24 April 2012      Published: 31 July 2012
PACS:  46.05.+b (General theory of continuum mechanics of solids)  
  02.20.Sv (Lie algebras of Lie groups)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/29/8/084601       OR      https://cpl.iphy.ac.cn/Y2012/V29/I8/084601
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Articles by authors
[1] Chand R, Davy D T and Ames W F 1976 Int. J. Nonlin. Mech. 11 191
[2] Ames W F and Suliciu I 1982 Int. J. Nonlin. Mech. 17 223
[3] Ames K A 1989 Int. J. Nonlin. Mech. 24 29
[4] Bokhari A H, Kara A H and Zaman F D 2007 Nonlin. Dyn. 48 49
[5] Ibragimov N H 1999 Elementary Lie group analysis and ordinary differential equations (New York: Wiley)
[6] Huang K F and Li H G 2012 Adv. Appl. Math. Mech. 4 382
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