2022
DOI: 10.3390/math10152759
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Lie Symmetry Analysis and Conservation Laws of the Axially Loaded Euler Beam

Abstract: By applying the Lie symmetry method, group-invariant solutions are constructed for axially loaded Euler beams. The corresponding mathematical models of the beams are formulated. After introducing the infinitesimal transformations, the determining equations of Lie symmetry are proposed via Lie point transformations acting on the original equations. The infinitesimal generators of symmetries of the systems are presented with Maple. The corresponding vector fields are given to span the subalgebra of the systems. … Show more

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Cited by 3 publications
(4 citation statements)
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“…Above denition has been interpreted from [21]. The innitesimal generator is used to dene the Lie algebra which is used for nding solutions for partial dierential equations [2,3,4,7] and for symmetry generating models [24].…”
Section: Denition 24 (Innitesimalsmentioning
confidence: 99%
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“…Above denition has been interpreted from [21]. The innitesimal generator is used to dene the Lie algebra which is used for nding solutions for partial dierential equations [2,3,4,7] and for symmetry generating models [24].…”
Section: Denition 24 (Innitesimalsmentioning
confidence: 99%
“…The applications of Lie symmetry analysis have been used in many research for solving nonlinear partial dierential equations found in physical problems [2,26,4,7,3,6,32,8] and for mathematical Models such as SIR models [33]. But in this project, we put a signicant emphasis on discussing the idea of symmetries of ODEs and demonstrate how their features can be used to obtain the exact solutions.…”
Section: −2ξmentioning
confidence: 99%
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