On conservation of energy and kinematic compatibility in dynamics of nonlinear velocity-based three-dimensional beams

Zupan, Eva (author), Zupan, Dejan (author)

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.

• Language: English
• Keywords: structural dynamics, non-linear beams, kinematic compatibility, energy conservation, rotational quaternions, implicit time integration
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2019
• Number of pages: Str. 1379-1394
• Numbering: Vol. 95, iss. 2
• PID: 20.500.12556/RUL-114090
• UDC: 624.04:624.072.2(045)
• ISSN on article: 0924-090X
• DOI: 10.1007/s11071-018-4634-y
• COBISS.SI-ID: 8601953
• Publication date in RUL: 13.02.2020

ZUPAN, Eva and ZUPAN, Dejan, 2019, On conservation of energy and kinematic compatibility in dynamics of nonlinear velocity-based three-dimensional beams. Nonlinear dynamics [online]. 2019. Vol. 95, no. 2, p. 1379–1394. [Accessed 3 April 2025]. DOI 10.1007/s11071-018-4634-y. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=114090

Record is a part of a journal

• Title: Nonlinear dynamics
• Shortened title: Nonlinear dyn.
• Publisher: Springer Nature
• ISSN: 0924-090X
• COBISS.SI-ID: 14632709

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
• Licensing start date: 30.01.2019

Secondary language

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

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P2-0260
• Name: Mehanika konstrukcij

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