Dispersion analysis of displacement-based and TDNNS mixed finite elements for thin-walled elastodynamics
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Dispersion analysis of displacement-based and TDNNS mixed finite elements for thin-walled elastodynamics
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA17-22615S" target="_blank" >GA17-22615S: Time reversal ultrasonic signal processing used in nondestructive evaluation of materials and structures</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematics and computers in simulation
ISSN
0378-4754
e-ISSN
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Volume of the periodical
189
Issue of the periodical within the volume
November
Country of publishing house
US - UNITED STATES
Number of pages
14
Pages from-to
325-338
UT code for WoS article
000683684700022
EID of the result in the Scopus database
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