Finite-element formulation of geometrically exact three-dimensional beam theories based on interpolation of strain measures

Zupan, Dejan (author), Saje, Miran (author)

This paper presents a new finite element formulation of the `geometrically exact finite-strain beam theory'. The governing equations of the beam element are derived in which the strain vectors are the only unknown functions. The consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal, is enforced to be satisfied at chosen points. The solution is found by a collocation algorithm. The linearity of the strain space not only simplifies the application of Newton's method on the non-linear configuration space, but also leads to the strain-objectivity of the proposed method. The accuracy and the efficiency of the derived numerical algorithm are demonstrated by several examples. (C) 2003 Elsevier B.V. All rights reserved.

• Language: English
• Keywords: non-linear beam theory, finite-element method, three-dimensional rotation, rotational invariant, strain measure
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publisher: Elsevier
• Year: 2003
• Number of pages: Str. [5209]-5248
• Numbering: Vol. 192, Vol. 192
• PID: 20.500.12556/RUL-32163
• UDC: 519.63:531.1
• ISSN on article: 0045-7825
• DOI: 10.1016/j.cma.2003.07.008
• COBISS.SI-ID: 2087265
• Publication date in RUL: 10.07.2015

ZUPAN, Dejan and SAJE, Miran, 2003, Finite-element formulation of geometrically exact three-dimensional beam theories based on interpolation of strain measures. Computer methods in applied mechanics and engineering [online]. 2003. Vol. 192, no. 192, p. 5209–5248. [Accessed 1 April 2025]. DOI 10.1016/j.cma.2003.07.008. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=32163

Record is a part of a journal

• Title: Computer methods in applied mechanics and engineering
• Shortened title: Comput. methods appl. mech. eng.
• Publisher: Elsevier
• ISSN: 0045-7825
• COBISS.SI-ID: 6695685

Secondary language

• Language: English
• Keywords: prostorski nosilci, točna teorija, nelinearnost, deformacije, metoda končnih elementov