Dispersion analysis of displacement-based and TDNNS mixed finite elements for thin-walled elastodynamics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F21%3A10248754" target="_blank" >RIV/61989100:27240/21:10248754 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S037847542100121X" target="_blank" >https://www.sciencedirect.com/science/article/pii/S037847542100121X</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.matcom.2021.04.003" target="_blank" >10.1016/j.matcom.2021.04.003</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Dispersion analysis of displacement-based and TDNNS mixed finite elements for thin-walled elastodynamics

Popis výsledku v původním jazyce

We compare several lowest-order finite element approximations to the problem of elastodynamics of thin-walled structures by means of dispersion analysis, which relates the parameter frequency-times-thickness (f d) and the wave speed. We restrict to analytical theory of harmonic front-crested waves that freely propagate in an infinite plate. Our study is formulated as a quasi-periodic eigenvalue problem on a single tensor-product element, which is eventually layered in the thickness direction. In the first part of the paper it is observed that the displacement-based finite elements align with the theory provided there are sufficiently many layers. In the second part we present novel anisotropic hexahedral tangential-displacement and normal- normal-stress continuous (TDNNS) mixed finite elements for Hellinger-Reissner formulation of elastodynamics. It turns out that one layer of such elements is sufficient for f d up to 2000 [kHz mm]. Nevertheless, due to a large amount of TDNNS degrees of freedom the computational complexity is only comparable to the multi-layer displacement-based element. This is not the case at low frequencies, where TDNNS is by far more efficient since it allows for rough anisotropic discretizations, contrary to the displacement-based elements that suffer from the shear locking effect. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Název v anglickém jazyce

Dispersion analysis of displacement-based and TDNNS mixed finite elements for thin-walled elastodynamics

Popis výsledku anglicky

We compare several lowest-order finite element approximations to the problem of elastodynamics of thin-walled structures by means of dispersion analysis, which relates the parameter frequency-times-thickness (f d) and the wave speed. We restrict to analytical theory of harmonic front-crested waves that freely propagate in an infinite plate. Our study is formulated as a quasi-periodic eigenvalue problem on a single tensor-product element, which is eventually layered in the thickness direction. In the first part of the paper it is observed that the displacement-based finite elements align with the theory provided there are sufficiently many layers. In the second part we present novel anisotropic hexahedral tangential-displacement and normal- normal-stress continuous (TDNNS) mixed finite elements for Hellinger-Reissner formulation of elastodynamics. It turns out that one layer of such elements is sufficient for f d up to 2000 [kHz mm]. Nevertheless, due to a large amount of TDNNS degrees of freedom the computational complexity is only comparable to the multi-layer displacement-based element. This is not the case at low frequencies, where TDNNS is by far more efficient since it allows for rough anisotropic discretizations, contrary to the displacement-based elements that suffer from the shear locking effect. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA17-22615S" target="_blank" >GA17-22615S: Využití časové reverzace ultrazvukových signálů v nedestruktivním hodnocení materiálů a konstrukcí</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Mathematics and computers in simulation

ISSN

0378-4754

e-ISSN

—

Svazek periodika

189

Číslo periodika v rámci svazku

November

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

325-338

Kód UT WoS článku

000683684700022

EID výsledku v databázi Scopus

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