In this paper, we study a finite-dimensional Lie point symmetry group of a system describing an ideal plastic plane flow in two dimensions in order to find analytical solutions. The infinitesimal generators that span this Lie algebra are given. We completely classify the subalgebras of codimension up to two into conjugacy classes under the action of the symmetry group. Based on invariant forms, we use Ansätze to compute symmetry reductions in such a way that the obtained solutions simultaneously cover many invariant and partially invariant solutions. We calculate solutions of algebraic, trigonometric, inverse trigonometric and elliptic type. Some solutions depending on one or two arbitrary functions of one variable have also been found. In some cases, the shape of a potentially feasible extrusion die corresponding to the solution is deduced. These tools could be used to thin, curve, undulate or shape a ring in an ideal plastic material.
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March 2012
Research Article|
March 08 2012
Symmetry group analysis of an ideal plastic flow
Vincent Lamothe
Vincent Lamothe
a)
Département de mathématiques et statistiques,
Université de Montréal
, C.P. 6128, Succc. Centre-ville, Montréal, (QC) H3C 3J7, Canada
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a)
Electronic mail: [email protected].
J. Math. Phys. 53, 033704 (2012)
Article history
Received:
February 08 2011
Accepted:
February 09 2012
Citation
Vincent Lamothe; Symmetry group analysis of an ideal plastic flow. J. Math. Phys. 1 March 2012; 53 (3): 033704. https://doi.org/10.1063/1.3690048
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