A consistent strain-based beam element with quaternion representation of rotations

Lolić, Damjan (author), Zupan, Dejan (author), Brojan, Miha (author)

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
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: In print
• Publication version: Author Accepted Manuscript
• Year: 2020
• Number of pages: Str. 1-16
• Numbering: Letn. XX, št. XX
• PID: 20.500.12556/RUL-114127
• UDC: 531/533:624
• ISSN on article: 0178-7675
• DOI: 10.1007/s00466-020-01826-0
• COBISS.SI-ID: 9081185
• Publication date in RUL: 18.02.2020

LOLIĆ, Damjan, ZUPAN, Dejan and BROJAN, Miha, 2020, A consistent strain-based beam element with quaternion representation of rotations. Computational mechanics [online]. 2020. Vol. XX, no. XX, p. 1–16. [Accessed 25 April 2025]. DOI 10.1007/s00466-020-01826-0. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=114127

Record is a part of a journal

• Title: Computational mechanics
• Shortened title: Comput. mech.
• Publisher: Springer
• ISSN: 0178-7675
• COBISS.SI-ID: 6668037

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

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P2-0263
• Name: Mehanika v tehniki

• Funder: ARRS - Slovenian Research Agency
• Project number: J2-8170
• Name: Nelinearna dinamika prostorskih okvirjev z izpolnjeno kinematično kompatibilnostjo za zahtevno uporabo v industriji