Dissimilar subalgebras of symmetry algebra of plasticity equations. (English) Zbl 07923135
Summary: In this paper we construct the optimal sets of dissimilar subalgebras up to dimension three for the Lie algebra of point symmetries of the system of three-dimensional stationary equations of perfect plasticity with the Huber-von Mises yield condition. The obtained results can be used to solve the problem of determining all invariant solutions of this system. It was necessary to design algorithms to facilitate some steps of the classification of subalgebras. The computational algebraic system SageMath was chosen to implement these algorithms. The most used functions and procedures are listed. The developed algorithms can be adapted to classify subalgebras of higher dimensions.
MSC:
| 08A30 | Subalgebras, congruence relations |
| 58J70 | Invariance and symmetry properties for PDEs on manifolds |
| 74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |
| 68W30 | Symbolic computation and algebraic computation |
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