Název: Inverse mass matrix for higher-order finite element method in linear free-vibration problems
Autoři: Kolman, Radek ; González, J.G. ; Cimrman, Robert ; Kopačka, Ján ; Cho, S.S. ; Park, B.G.
Typ dokumentu: Příspěvky z konference
Konference/Akce: International Conference Engineering Mechanics 2020 /26./, Brno (CZ), 20201124
Rok: 2020
Jazyk: eng
Abstrakt: 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.
Klíčová slova: consistent and lumped massmatrix; direct inverse mass matrix; free vibration problem; heterogeneous bar; higher-order finite element method
Číslo projektu: GC19-02288J (CEP)
Poskytovatel projektu: GA ČR
Zdrojový dokument: ENGINEERING MECHANICS 2020, ISBN 978-80-214-5896-3, ISSN 1805-8248
Poznámka: Související webová stránka: https://www.engmech.cz/im/im/page/proc

Instituce: Ústav termomechaniky AV ČR (web)
Informace o dostupnosti dokumentu: Dokument je dostupný v příslušném ústavu Akademie věd ČR.
Původní záznam: http://hdl.handle.net/11104/0315951

Trvalý odkaz NUŠL: http://www.nusl.cz/ntk/nusl-432656


Záznam je zařazen do těchto sbírek:
Věda a výzkum > AV ČR > Ústav termomechaniky
Konferenční materiály > Příspěvky z konference