Higher-Order Invariant Manifold Parametrisation of Geometrically Nonlinear Structures Modelled with Large Finite Element Models

Alessandra Vizzaccaro; Andrea Opreni; Loic Salles; Attilio Frangi; Cyril Touzé

doi:10.1007/978-3-031-04086-3_32

Higher-Order Invariant Manifold Parametrisation of Geometrically Nonlinear Structures Modelled with Large Finite Element Models

Alessandra Vizzaccaro
, Andrea Opreni
, Loic Salles
, Attilio Frangi
, Cyril Touzé

Imperial College London
University of Bristol
Politecnico di Milano
Skolkovo Institute of Science and Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this contribution we present a method to directly compute asymptotic expansion of invariant manifolds of large finite element models from physical coordinates and their reduced-order dynamics on the manifold. We show the accuracy of the reduction on selected models, exhibiting large rotations and internal resonances. The results obtained with the reduction are compared to full-order harmonic balance simulations obtained by continuation of the forced response. We also illustrate the low computational cost of the present implementation for increasing order of the asymptotic expansion and increasing number of degrees of freedom in the structure. The results presented show that the proposed methodology can reproduce extremely accurately the dynamics of the systems with a very low computational cost.

Original language	English
Title of host publication	Nonlinear Structures and Systems, Volume 1 - Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022
Editors	Matthew R.W. Brake, Ludovic Renson, Robert J. Kuether, Paolo Tiso
Publisher	Springer
Pages	233-236
Number of pages	4
ISBN (Print)	9783031040856
DOIs	https://doi.org/10.1007/978-3-031-04086-3_32
Publication status	Published - 1 Jan 2023
Event	40th IMAC, A Conference and Exposition on Structural Dynamics, 2022 - Orlando, United States Duration: 7 Feb 2022 → 10 Feb 2022

Publication series

Name	Conference Proceedings of the Society for Experimental Mechanics Series
ISSN (Print)	2191-5644
ISSN (Electronic)	2191-5652

Conference

Conference	40th IMAC, A Conference and Exposition on Structural Dynamics, 2022
Country/Territory	United States
City	Orlando
Period	7/02/22 → 10/02/22

Keywords

Direct parametrisation
Invariant manifold
Large-scale FE models
Reduced-order modelling

Access to Document

10.1007/978-3-031-04086-3_32

Cite this

Vizzaccaro, A., Opreni, A., Salles, L., Frangi, A., & Touzé, C. (2023). Higher-Order Invariant Manifold Parametrisation of Geometrically Nonlinear Structures Modelled with Large Finite Element Models. In M. R. W. Brake, L. Renson, R. J. Kuether, & P. Tiso (Eds.), Nonlinear Structures and Systems, Volume 1 - Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022 (pp. 233-236). (Conference Proceedings of the Society for Experimental Mechanics Series). Springer. https://doi.org/10.1007/978-3-031-04086-3_32

Vizzaccaro, Alessandra ; Opreni, Andrea ; Salles, Loic et al. / Higher-Order Invariant Manifold Parametrisation of Geometrically Nonlinear Structures Modelled with Large Finite Element Models. Nonlinear Structures and Systems, Volume 1 - Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022. editor / Matthew R.W. Brake ; Ludovic Renson ; Robert J. Kuether ; Paolo Tiso. Springer, 2023. pp. 233-236 (Conference Proceedings of the Society for Experimental Mechanics Series).

@inproceedings{ad17d21978a641fc984fa13917343076,

title = "Higher-Order Invariant Manifold Parametrisation of Geometrically Nonlinear Structures Modelled with Large Finite Element Models",

abstract = "In this contribution we present a method to directly compute asymptotic expansion of invariant manifolds of large finite element models from physical coordinates and their reduced-order dynamics on the manifold. We show the accuracy of the reduction on selected models, exhibiting large rotations and internal resonances. The results obtained with the reduction are compared to full-order harmonic balance simulations obtained by continuation of the forced response. We also illustrate the low computational cost of the present implementation for increasing order of the asymptotic expansion and increasing number of degrees of freedom in the structure. The results presented show that the proposed methodology can reproduce extremely accurately the dynamics of the systems with a very low computational cost.",

keywords = "Direct parametrisation, Invariant manifold, Large-scale FE models, Reduced-order modelling",

author = "Alessandra Vizzaccaro and Andrea Opreni and Loic Salles and Attilio Frangi and Cyril Touz{\'e}",

note = "Publisher Copyright: {\textcopyright} 2023, The Society for Experimental Mechanics, Inc.; 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022 ; Conference date: 07-02-2022 Through 10-02-2022",

year = "2023",

month = jan,

day = "1",

doi = "10.1007/978-3-031-04086-3\_32",

language = "English",

isbn = "9783031040856",

series = "Conference Proceedings of the Society for Experimental Mechanics Series",

publisher = "Springer",

pages = "233--236",

editor = "Brake, \{Matthew R.W.\} and Ludovic Renson and Kuether, \{Robert J.\} and Paolo Tiso",

booktitle = "Nonlinear Structures and Systems, Volume 1 - Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022",

}

Vizzaccaro, A, Opreni, A, Salles, L, Frangi, A & Touzé, C 2023, Higher-Order Invariant Manifold Parametrisation of Geometrically Nonlinear Structures Modelled with Large Finite Element Models. in MRW Brake, L Renson, RJ Kuether & P Tiso (eds), Nonlinear Structures and Systems, Volume 1 - Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022. Conference Proceedings of the Society for Experimental Mechanics Series, Springer, pp. 233-236, 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022, Orlando, United States, 7/02/22. https://doi.org/10.1007/978-3-031-04086-3_32

Higher-Order Invariant Manifold Parametrisation of Geometrically Nonlinear Structures Modelled with Large Finite Element Models. / Vizzaccaro, Alessandra; Opreni, Andrea; Salles, Loic et al.
Nonlinear Structures and Systems, Volume 1 - Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022. ed. / Matthew R.W. Brake; Ludovic Renson; Robert J. Kuether; Paolo Tiso. Springer, 2023. p. 233-236 (Conference Proceedings of the Society for Experimental Mechanics Series).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Higher-Order Invariant Manifold Parametrisation of Geometrically Nonlinear Structures Modelled with Large Finite Element Models

AU - Vizzaccaro, Alessandra

AU - Opreni, Andrea

AU - Salles, Loic

AU - Frangi, Attilio

AU - Touzé, Cyril

PY - 2023/1/1

Y1 - 2023/1/1

N2 - In this contribution we present a method to directly compute asymptotic expansion of invariant manifolds of large finite element models from physical coordinates and their reduced-order dynamics on the manifold. We show the accuracy of the reduction on selected models, exhibiting large rotations and internal resonances. The results obtained with the reduction are compared to full-order harmonic balance simulations obtained by continuation of the forced response. We also illustrate the low computational cost of the present implementation for increasing order of the asymptotic expansion and increasing number of degrees of freedom in the structure. The results presented show that the proposed methodology can reproduce extremely accurately the dynamics of the systems with a very low computational cost.

AB - In this contribution we present a method to directly compute asymptotic expansion of invariant manifolds of large finite element models from physical coordinates and their reduced-order dynamics on the manifold. We show the accuracy of the reduction on selected models, exhibiting large rotations and internal resonances. The results obtained with the reduction are compared to full-order harmonic balance simulations obtained by continuation of the forced response. We also illustrate the low computational cost of the present implementation for increasing order of the asymptotic expansion and increasing number of degrees of freedom in the structure. The results presented show that the proposed methodology can reproduce extremely accurately the dynamics of the systems with a very low computational cost.

KW - Direct parametrisation

KW - Invariant manifold

KW - Large-scale FE models

KW - Reduced-order modelling

UR - https://www.scopus.com/pages/publications/85135872622

U2 - 10.1007/978-3-031-04086-3_32

DO - 10.1007/978-3-031-04086-3_32

M3 - Conference contribution

AN - SCOPUS:85135872622

SN - 9783031040856

T3 - Conference Proceedings of the Society for Experimental Mechanics Series

SP - 233

EP - 236

BT - Nonlinear Structures and Systems, Volume 1 - Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022

A2 - Brake, Matthew R.W.

A2 - Renson, Ludovic

A2 - Kuether, Robert J.

A2 - Tiso, Paolo

PB - Springer

T2 - 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022

Y2 - 7 February 2022 through 10 February 2022

ER -

Vizzaccaro A, Opreni A, Salles L, Frangi A, Touzé C. Higher-Order Invariant Manifold Parametrisation of Geometrically Nonlinear Structures Modelled with Large Finite Element Models. In Brake MRW, Renson L, Kuether RJ, Tiso P, editors, Nonlinear Structures and Systems, Volume 1 - Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022. Springer. 2023. p. 233-236. (Conference Proceedings of the Society for Experimental Mechanics Series). doi: 10.1007/978-3-031-04086-3_32

Higher-Order Invariant Manifold Parametrisation of Geometrically Nonlinear Structures Modelled with Large Finite Element Models

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this