Higher-order inverse mass matrices for the explicit transient analysis of heterogeneous solids

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61388998%3A_____%2F24%3A00585736" target="_blank" >RIV/61388998:_____/24:00585736 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/71226401:_____/24:N0100936

Výsledek na webu

<a href="https://onlinelibrary.wiley.com/doi/10.1002/nme.7457" target="_blank" >https://onlinelibrary.wiley.com/doi/10.1002/nme.7457</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/nme.7457" target="_blank" >10.1002/nme.7457</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Higher-order inverse mass matrices for the explicit transient analysis of heterogeneous solids

Popis výsledku v původním jazyce

New methods are presented for the direct computation of higher-order inverse mass matrices (also called reciprocal mass matrices) that are used for explicit transient finite element analysis. The motivation of this work lies in the need of having appropriate sparse inverse mass matrices, which present the same structure as the consistent mass matrix, preserve the total mass, predict suitable frequency spectrum and dictate sufficiently large critical time step sizes. For an efficient evaluation of the reciprocal mass matrix, the projection matrix should be diagonal. This condition can be satisfied by adopting dual shape functions for the momentum field, generated from the same shape functions used for the displacement field. A theoretically consistent derivation of the inverse mass matrix is based on the three-field Hamilton principle and requires the projection matrix to be evaluated from the integral of these shape functions. Unfortunately, for higher-order FE shape functions and serendipity FE elements, the projection matrix is not positive definitive and can not be employed. Therefore, we study several lumping procedures for higher order reciprocal mass matrices considering their effect on total-mass preserving, frequency spectra and accuracy in explicit transient simulations. The article closes with several numerical examples showing suitability of the direct inverse mass matrix in dynamics.

Název v anglickém jazyce

Higher-order inverse mass matrices for the explicit transient analysis of heterogeneous solids

Popis výsledku anglicky

New methods are presented for the direct computation of higher-order inverse mass matrices (also called reciprocal mass matrices) that are used for explicit transient finite element analysis. The motivation of this work lies in the need of having appropriate sparse inverse mass matrices, which present the same structure as the consistent mass matrix, preserve the total mass, predict suitable frequency spectrum and dictate sufficiently large critical time step sizes. For an efficient evaluation of the reciprocal mass matrix, the projection matrix should be diagonal. This condition can be satisfied by adopting dual shape functions for the momentum field, generated from the same shape functions used for the displacement field. A theoretically consistent derivation of the inverse mass matrix is based on the three-field Hamilton principle and requires the projection matrix to be evaluated from the integral of these shape functions. Unfortunately, for higher-order FE shape functions and serendipity FE elements, the projection matrix is not positive definitive and can not be employed. Therefore, we study several lumping procedures for higher order reciprocal mass matrices considering their effect on total-mass preserving, frequency spectra and accuracy in explicit transient simulations. The article closes with several numerical examples showing suitability of the direct inverse mass matrix in dynamics.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20302 - Applied mechanics

Projekt

<a href="/cs/project/GA23-06220S" target="_blank" >GA23-06220S: Flexoelektrické periodické struktury pro transport tekutin a sběr energie</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

International Journal for Numerical Methods in Engineering

ISSN

0029-5981

e-ISSN

1097-0207

Svazek periodika

125

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

25

Strana od-do

e7457

Kód UT WoS článku

001162858400001

EID výsledku v databázi Scopus

2-s2.0-85185680561