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Original title:
Inverse mass matrix for higher-order finite element method in linear free-vibration problems
Authors: Kolman, Radek ; González, J.G. ; Cimrman, Robert ; Kopačka, Ján ; Cho, S.S. ; Park, B.G.
Document type: Papers
Conference/Event: International Conference Engineering Mechanics 2020 /26./, Brno (CZ), 20201124
Year: 2020
Language: eng
Abstract: In the paper, we present adirect inverse mass matrix in the higher-orderfinite element method forsolid mechanics. The direct inverse mass matrix is sparse, has the same structure as the consistent mass matrixand preserves the total mass. The core of derivation of the semi-discrete mixed form is based on the Hamilton’s principle of leastaction. The cardinal issue is finding the relationship between discretized velocities and discretized linear momentum. Finally, the simple formula for the direct inversemass matrix is presented as well as thechoice of density-weighted dual shape functions for linear momentum with respect to the displacement shape functionwith achoice of the lumping mass method for obtaining the correct and positive definitive velocity-linear momentum operator. The application of Dirichlet boundaryconditions into the direct inversemass matrix forafloating system is achieved usingthe projection operator. The suggested methodology is tested on a free-vibration problem of heterogeneous bar for different ordersof shape functions.
Keywords: consistent and lumped massmatrix; direct inverse mass matrix; free vibration problem; heterogeneous bar; higher-order finite element method
Project no.: GC19-02288J (CEP)
Funding provider: GA ČR
Host item entry: ENGINEERING MECHANICS 2020, ISBN 978-80-214-5896-3, ISSN 1805-8248
Note: Související webová stránka: https://www.engmech.cz/im/im/page/proc
Institution: Institute of Thermomechanics AS ČR (web)
Document availability information: Fulltext is available at the institute of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0315951
Permalink: http://www.nusl.cz/ntk/nusl-432656
The record appears in these collections:
Research > Institutes ASCR > Institute of Thermomechanics
Conference materials > Papers
Authors: Kolman, Radek ; González, J.G. ; Cimrman, Robert ; Kopačka, Ján ; Cho, S.S. ; Park, B.G.
Document type: Papers
Conference/Event: International Conference Engineering Mechanics 2020 /26./, Brno (CZ), 20201124
Year: 2020
Language: eng
Abstract: In the paper, we present adirect inverse mass matrix in the higher-orderfinite element method forsolid mechanics. The direct inverse mass matrix is sparse, has the same structure as the consistent mass matrixand preserves the total mass. The core of derivation of the semi-discrete mixed form is based on the Hamilton’s principle of leastaction. The cardinal issue is finding the relationship between discretized velocities and discretized linear momentum. Finally, the simple formula for the direct inversemass matrix is presented as well as thechoice of density-weighted dual shape functions for linear momentum with respect to the displacement shape functionwith achoice of the lumping mass method for obtaining the correct and positive definitive velocity-linear momentum operator. The application of Dirichlet boundaryconditions into the direct inversemass matrix forafloating system is achieved usingthe projection operator. The suggested methodology is tested on a free-vibration problem of heterogeneous bar for different ordersof shape functions.
Keywords: consistent and lumped massmatrix; direct inverse mass matrix; free vibration problem; heterogeneous bar; higher-order finite element method
Project no.: GC19-02288J (CEP)
Funding provider: GA ČR
Host item entry: ENGINEERING MECHANICS 2020, ISBN 978-80-214-5896-3, ISSN 1805-8248
Note: Související webová stránka: https://www.engmech.cz/im/im/page/proc
Institution: Institute of Thermomechanics AS ČR (web)
Document availability information: Fulltext is available at the institute of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0315951
Permalink: http://www.nusl.cz/ntk/nusl-432656
The record appears in these collections:
Research > Institutes ASCR > Institute of Thermomechanics
Conference materials > Papers
Record created 2021-02-24, last modified 2022-09-29