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A consistent strain-based beam element with quaternion representation of rotations
Lolić, Damjan (Author), Zupan, Dejan (Author), Brojan, Miha (Author)

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Abstract
We present a novel consistent singularity-free strain-based finite element formulation for the analysis of three-dimensional frame-like structures. Our model is based on a geometrically exact finite-strain beam theory, quaternion parametrization of spatial rotations, assumption that the strain measures are constant along the length of the element and a proper choice of basis for the translational strain vector representation. As it is common for strain-based elements, the present formulation does not suffer from shear locking. A comparison of our results with the results from the literature and a commercial finite element analysis software demonstrates the advantages of the proposed formulation, especially when the structure is subjected to larger shear deformations. This stems from the fact that our model ensures a mathematically consistent updating procedure for all the quantities describing the beam. This aspect is often overlooked, since most of the numerical cases from other studies on this topic engage rather small-shear strains for which the consistent update is not crucial as the number of elements is increased.

Language:English
Keywords:non-linear beams, rotational quaternions, strain vectors, global basis description
Work type:Scientific work (r2)
Tipology:1.01 - Original Scientific Article
Organization:FGG - Faculty of Civil and Geodetic Engineering
Year:2020
Number of pages:Str. 1-16
Numbering:Letn. XX, št. XX
UDC:531/533:624
ISSN on article:0178-7675
DOI:10.1007/s00466-020-01826-0 This link opens in a new window
COBISS.SI-ID:9081185 This link opens in a new window
Views:281
Downloads:133
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Record is a part of a journal

Title:Computational mechanics
Shortened title:Comput. mech.
Publisher:Springer
ISSN:0178-7675
COBISS.SI-ID:6668037 This link opens in a new window

Document is financed by a project

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Project no.:P2-0263
Name:Mehanika v tehniki

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Project no.:J2-8170
Name:Nelinearna dinamika prostorskih okvirjev z izpolnjeno kinematično kompatibilnostjo za zahtevno uporabo v industriji

Licences

License:CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Link:http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
Licensing start date:18.02.2020

Secondary language

Language:Slovenian
Keywords:nelinearni nosilci, rotacijski kvaternioni, deformacijski vektorji, opis v fiksni bazi

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