Mixed finite elements for port-Hamiltonian models of von Kármán beams

Andrea Brugnoli; Ramy Rashad; Federico Califano; Stefano Stramigioli; Denis Matignon

doi:10.1016/j.ifacol.2021.11.076

Mixed finite elements for port-Hamiltonian models of von Kármán beams

Andrea Brugnoli^*, Ramy Rashad, Federico Califano, Stefano Stramigioli, Denis Matignon

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › Academic › peer-review

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Abstract

A port-Hamiltonian formulation of von Kármán beams is presented. The variables selection lead to a non linear interconnection operator, while the constitutive laws are linear. The model can be readily discretized by exploiting a coenergy formulation and a mixed finite element method. The mixed formulation does not demand the H² regularity requirement typical of standard Galerkin discretization of thin structures. A numerical test is performed to assess the convergence rate of the solution.

Original language	English
Pages (from-to)	186-191
Number of pages	6
Journal	IFAC-papersonline
Volume	54
Issue number	19
Early online date	19 Nov 2021
DOIs	https://doi.org/10.1016/j.ifacol.2021.11.076
Publication status	Published - 2021
Event	7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021 - Berlin, Germany Duration: 11 Oct 2021 → 13 Oct 2021

Keywords

Mixed finite elements
Port-Hamiltonian systems
Von Kármán beams

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10.1016/j.ifacol.2021.11.076Licence: CC BY-NC-ND

ArticleFinal published version, 1.14 MBLicence: CC BY-NC-ND

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title = "Mixed finite elements for port-Hamiltonian models of von K{\'a}rm{\'a}n beams",

abstract = "A port-Hamiltonian formulation of von K{\'a}rm{\'a}n beams is presented. The variables selection lead to a non linear interconnection operator, while the constitutive laws are linear. The model can be readily discretized by exploiting a coenergy formulation and a mixed finite element method. The mixed formulation does not demand the H2 regularity requirement typical of standard Galerkin discretization of thin structures. A numerical test is performed to assess the convergence rate of the solution.",

keywords = "Mixed finite elements, Port-Hamiltonian systems, Von K{\'a}rm{\'a}n beams",

author = "Andrea Brugnoli and Ramy Rashad and Federico Califano and Stefano Stramigioli and Denis Matignon",

note = "Funding Information: Thifi work wafi fiupported ffiΩ the PortWingfi project funded ffiΩ the European Refiearch Council [Grant Agreement No. 787675] REFERENCES R. Altmann and P. Schulze. A port-Hamiltonian for-mulation of the Navier–Stokefi equationfi for reac-tive flowfi. Systems & Control Letters, 100:51 – 55, 2017. ISSN 0167-6911. doi: httpfi://doi.org/10.1016/ j.fiΩficonle.2016.12.005. Publisher Copyright: {\textcopyright} The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/); 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021 ; Conference date: 11-10-2021 Through 13-10-2021",

year = "2021",

doi = "10.1016/j.ifacol.2021.11.076",

language = "English",

volume = "54",

pages = "186--191",

journal = "IFAC-papersonline",

issn = "2405-8963",

publisher = "IFAC Secretariat",

number = "19",

}

TY - JOUR

T1 - Mixed finite elements for port-Hamiltonian models of von Kármán beams

AU - Brugnoli, Andrea

AU - Rashad, Ramy

AU - Califano, Federico

AU - Stramigioli, Stefano

AU - Matignon, Denis

N1 - Funding Information: Thifi work wafi fiupported ffiΩ the PortWingfi project funded ffiΩ the European Refiearch Council [Grant Agreement No. 787675] REFERENCES R. Altmann and P. Schulze. A port-Hamiltonian for-mulation of the Navier–Stokefi equationfi for reac-tive flowfi. Systems & Control Letters, 100:51 – 55, 2017. ISSN 0167-6911. doi: httpfi://doi.org/10.1016/ j.fiΩficonle.2016.12.005. Publisher Copyright: © The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)

PY - 2021

Y1 - 2021

N2 - A port-Hamiltonian formulation of von Kármán beams is presented. The variables selection lead to a non linear interconnection operator, while the constitutive laws are linear. The model can be readily discretized by exploiting a coenergy formulation and a mixed finite element method. The mixed formulation does not demand the H2 regularity requirement typical of standard Galerkin discretization of thin structures. A numerical test is performed to assess the convergence rate of the solution.

AB - A port-Hamiltonian formulation of von Kármán beams is presented. The variables selection lead to a non linear interconnection operator, while the constitutive laws are linear. The model can be readily discretized by exploiting a coenergy formulation and a mixed finite element method. The mixed formulation does not demand the H2 regularity requirement typical of standard Galerkin discretization of thin structures. A numerical test is performed to assess the convergence rate of the solution.

KW - Mixed finite elements

KW - Port-Hamiltonian systems

KW - Von Kármán beams

UR - http://www.scopus.com/inward/record.url?scp=85120951667&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2021.11.076

DO - 10.1016/j.ifacol.2021.11.076

M3 - Conference article

AN - SCOPUS:85120951667

VL - 54

SP - 186

EP - 191

JO - IFAC-papersonline

JF - IFAC-papersonline

SN - 2405-8963

IS - 19

T2 - 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021

Y2 - 11 October 2021 through 13 October 2021

ER -

Mixed finite elements for port-Hamiltonian models of von Kármán beams

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