Inverse mass matrix for higher-order finite element method in linear free-vibration problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61388998%3A_____%2F20%3A00537536" target="_blank" >RIV/61388998:_____/20:00537536 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.engmech.cz/im/im/page/proc" target="_blank" >https://www.engmech.cz/im/im/page/proc</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.21495/5896-3-282" target="_blank" >10.21495/5896-3-282</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Inverse mass matrix for higher-order finite element method in linear free-vibration problems

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Inverse mass matrix for higher-order finite element method in linear free-vibration problems

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

20302 - Applied mechanics

Projekt

<a href="/cs/project/GC19-02288J" target="_blank" >GC19-02288J: Robustní metody redukce-řádu modelu pro úlohy interakce poddajných těles s tekutinou</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

ENGINEERING MECHANICS 2020

ISBN

978-80-214-5896-3

ISSN

1805-8248

e-ISSN

—

Počet stran výsledku

4

Strana od-do

282-285

Název nakladatele

Brno University of Technology Institute of Solid Mechanics, Mechatronics and Biomechanics

Místo vydání

Brno

Místo konání akce

Brno

Datum konání akce

24. 11. 2020

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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