Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures
The aim of this contribution is to present numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures. Three different methods are compared: the implicit condensation and expansion (ICE), the quadratic mani...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-03-01
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| Series: | Vibration |
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| Online Access: | https://www.mdpi.com/2571-631X/4/1/14 |
| _version_ | 1797414153747431424 |
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| author | Yichang Shen Alessandra Vizzaccaro Nassim Kesmia Ting Yu Loïc Salles Olivier Thomas Cyril Touzé |
| author_facet | Yichang Shen Alessandra Vizzaccaro Nassim Kesmia Ting Yu Loïc Salles Olivier Thomas Cyril Touzé |
| author_sort | Yichang Shen |
| collection | DOAJ |
| description | The aim of this contribution is to present numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures. Three different methods are compared: the implicit condensation and expansion (ICE), the quadratic manifold computed from modal derivatives (MD), and the direct normal form (DNF) procedure, the latter expressing the reduced dynamics in an invariant-based span of the phase space. The methods are first presented in order to underline their common points and differences, highlighting in particular that ICE and MD use reduction subspaces that are not invariant. A simple analytical example is then used in order to analyze how the different treatments of quadratic nonlinearities by the three methods can affect the predictions. Finally, three beam examples are used to emphasize the ability of the methods to handle curvature (on a curved beam), 1:1 internal resonance (on a clamped-clamped beam with two polarizations), and inertia nonlinearity (on a cantilever beam). |
| first_indexed | 2024-03-09T05:29:00Z |
| format | Article |
| id | doaj.art-16c880984fad43e8a65b9512d5bfe2be |
| institution | Directory Open Access Journal |
| issn | 2571-631X |
| language | English |
| last_indexed | 2024-03-09T05:29:00Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Vibration |
| spelling | doaj.art-16c880984fad43e8a65b9512d5bfe2be2023-12-03T12:34:02ZengMDPI AGVibration2571-631X2021-03-014117520410.3390/vibration4010014Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam StructuresYichang Shen0Alessandra Vizzaccaro1Nassim Kesmia2Ting Yu3Loïc Salles4Olivier Thomas5Cyril Touzé6Institut of Mechanical Sciences and Industrial Applications (IMSIA), ENSTA Paris, CNRS, EDF, CEA, Institut Polytechnique de Paris, 91762 Palaiseau, FranceVibration University Technology Centre, Imperial College London, London SW7 2AZ, UKInstitut of Mechanical Sciences and Industrial Applications (IMSIA), ENSTA Paris, CNRS, EDF, CEA, Institut Polytechnique de Paris, 91762 Palaiseau, FranceInstitut of Mechanical Sciences and Industrial Applications (IMSIA), ENSTA Paris, CNRS, EDF, CEA, Institut Polytechnique de Paris, 91762 Palaiseau, FranceVibration University Technology Centre, Imperial College London, London SW7 2AZ, UKArts et Métiers Institute of Technology, LISPEN, HESAM Université, 8 boulevard Louis XIV, 59000 Lille, FranceInstitut of Mechanical Sciences and Industrial Applications (IMSIA), ENSTA Paris, CNRS, EDF, CEA, Institut Polytechnique de Paris, 91762 Palaiseau, FranceThe aim of this contribution is to present numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures. Three different methods are compared: the implicit condensation and expansion (ICE), the quadratic manifold computed from modal derivatives (MD), and the direct normal form (DNF) procedure, the latter expressing the reduced dynamics in an invariant-based span of the phase space. The methods are first presented in order to underline their common points and differences, highlighting in particular that ICE and MD use reduction subspaces that are not invariant. A simple analytical example is then used in order to analyze how the different treatments of quadratic nonlinearities by the three methods can affect the predictions. Finally, three beam examples are used to emphasize the ability of the methods to handle curvature (on a curved beam), 1:1 internal resonance (on a clamped-clamped beam with two polarizations), and inertia nonlinearity (on a cantilever beam).https://www.mdpi.com/2571-631X/4/1/14reduced-order modeldirect normal formgeometric nonlinearitymodal derivativesimplicit condensation and expansion |
| spellingShingle | Yichang Shen Alessandra Vizzaccaro Nassim Kesmia Ting Yu Loïc Salles Olivier Thomas Cyril Touzé Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures Vibration reduced-order model direct normal form geometric nonlinearity modal derivatives implicit condensation and expansion |
| title | Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures |
| title_full | Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures |
| title_fullStr | Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures |
| title_full_unstemmed | Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures |
| title_short | Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures |
| title_sort | comparison of reduction methods for finite element geometrically nonlinear beam structures |
| topic | reduced-order model direct normal form geometric nonlinearity modal derivatives implicit condensation and expansion |
| url | https://www.mdpi.com/2571-631X/4/1/14 |
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