On conservation of energy and kinematic compatibility in dynamics of nonlinear velocity-based three-dimensional beams
Zupan, Eva (Author), Zupan, Dejan (Author)

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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:structural dynamics, non-linear beams, kinematic compatibility, energy conservation, rotational quaternions, implicit time integration
Work type:Scientific work (r2)
Tipology:1.01 - Original Scientific Article
Organization:FGG - Faculty of Civil and Geodetic Engineering
Number of pages:str. 1379-1394
Numbering:Letn. 95, št. 2
ISSN on article:0924-090X
DOI:10.1007/s11071-018-4634-y Link is opened in a new window
COBISS.SI-ID:8601953 Link is opened in a new window
License:CC BY-NC-ND 4.0
This work is available under this license: Creative Commons Attribution Non-Commercial No Derivatives 4.0 International
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Record is a part of a journal

Title:Nonlinear dynamics
Shortened title:Nonlinear dyn.
Publisher:Kluwer Academic Publishers
COBISS.SI-ID:14632709 This link opens in a new window

Document is financed by a project

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

Secondary language

Keywords:dinamika konstrukcij, nelinearni nosilci, kinematična kompatibilnost, ohranjanje energije, rotacijski kvaternioni, implicitna časovna integracija

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