Eva Zupan (Author), Dejan Zupan (Author)

Abstract

In this paper, we present an original energypreserving numerical formulation for velocity-based geometrically exact three-dimensional beams. We employ the algebra of quaternions as a suitable tool to express the governing equations and relate rotations with their derivatives,while the finite-element discretization is based on interpolation of velocities in a fixed frame and angular velocities in a moving frame description. The proposed time discretization of governing equations directly relates the energy conservation constraint with the time-discrete kinematic compatibility equations. We show that a suitable choice of primary unknowns together with a convenient choice of the frame of reference for quantities and equations is beneficial for the conservation of energy and enables admissible approximations in a simple manner and without any additional effort. The result of this study is simple and efficient, yet accurate and robust numerical model.

Keywords

dinamika konstrukcij;nelinearni nosilci;kinematična kompatibilnost;ohranjanje energije;rotacijski kvaternioni;implicitna časovna integracija;structural dynamics;non-linear beams;kinematic compatibility;energy conservation;rotational quaternions;implicit time integration;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FGG - Faculty of Civil and Geodetic Engineering
UDC: 624.04:624.072.2(045)
COBISS: 8601953 Link will open in a new window
ISSN: 0924-090X
Views: 831
Downloads: 441
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Other data

Secondary language: Slovenian
Secondary keywords: dinamika konstrukcij;nelinearni nosilci;kinematična kompatibilnost;ohranjanje energije;rotacijski kvaternioni;implicitna časovna integracija;
Type (COBISS): Article
Pages: str. 1379-1394
Volume: ǂLetn. ǂ95
Issue: ǂšt. ǂ2
Chronology: jan. 2019
DOI: 10.1007/s11071-018-4634-y
ID: 11407618