Dynamics of 3D beam elements in a corotational context: A comparative study of established and new formulations
2012 (English)In: Finite elements in analysis and design (Print), ISSN 0168-874X, Vol. 61, 97-111 p.Article in journal (Refereed) Published
This paper deals with Newmark time stepping methods and finite rotations for nonlinear finite element analysis of flexible beam structures. The corotational method is used to develop expressions of the internal forces and the corresponding tangent stiffness matrices. For the dynamic part, four formulations based on different parameterizations of rotations are compared. The first three are classic formulations taken from the literature with some modifications for two of them. The last one is new and uses three of the four Euler parameters (quaternion) as rotational variables. For all these approaches, theoretical derivations as well as practical implementations are given in detail. The similarities and differences between the formulations are pointed out. Six numerical examples are studied in order to compare these four formulations in terms of numerical accuracy and computational efficiency. Regarding efficiency, the choice of the predictor at each time step and the possibility to simplify the tangent inertia matrix are carefully investigated. The numerical results show that these four formulations have the same numerical accuracy, but that the computational efficiency depends on the choice of the tangent inertia matrix. Besides, the new formulation proposed in this paper turns out to be the fastest one.
Place, publisher, year, edition, pages
2012. Vol. 61, 97-111 p.
Time stepping method, finite rotations, nonlinear dynamics, 3D beam elements
IdentifiersURN: urn:nbn:se:kth:diva-95197DOI: 10.1016/j.finel.2012.06.007ISI: 000307825900010ScopusID: 2-s2.0-84864428298OAI: oai:DiVA.org:kth-95197DiVA: diva2:527070
QC 20120829. Updated from submitted to published.2012-05-162012-05-162013-10-17Bibliographically approved