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

0537536 - ÚT 2021 RIV CZ eng C - Conference Paper (international conference)
Kolman, Radek - González, J.G. - Cimrman, Robert - Kopačka, Ján - Cho, S.S. - Park, B.G.
Inverse mass matrix for higher-order finite element method in linear free-vibration problems.
ENGINEERING MECHANICS 2020. Brno: Brno University of Technology Institute of Solid Mechanics, Mechatronics and Biomechanics, 2020 - (Fuis, V.), s. 282-285. ISBN 978-80-214-5896-3. ISSN 1805-8248.
[International Conference Engineering Mechanics 2020 /26./. Brno (CZ), 24.11.2020-25.11.2020]
R&D Projects: GA ČR(CZ) GC19-02288J
Institutional support: RVO:61388998
Keywords : higher-order finite element method * direct inverse mass matrix * consistent and lumped massmatrix * free vibration problem * heterogeneous bar
OECD category: Applied mechanics
https://www.engmech.cz/im/im/page/proc

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.
Permanent Link: http://hdl.handle.net/11104/0315951