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Interpolation of rotational variables in nonlinear dynamics of 3D beams
Author(s) -
Jelenić G.,
Crisfield M. A.
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19981215)43:7<1193::aid-nme463>3.0.co;2-p
Subject(s) - interpolation (computer graphics) , rotation (mathematics) , stability (learning theory) , nonlinear system , transformation (genetics) , mathematics , space (punctuation) , algorithm , computer science , algebra over a field , geometry , motion (physics) , physics , artificial intelligence , pure mathematics , biochemistry , chemistry , quantum mechanics , machine learning , gene , operating system
Abstract The formulation of dynamic procedures for three‐dimensional (3‐D) beams requires extensive use of the algebra pertaining to the non‐linear character of the rotation group in space. The corresponding extraction procedure to obtain the rotations that span a time step has certain limitations, which can have a detrimental effect on the overall stability of a time‐integration scheme. The paper describes two algorithms for the dynamics of 3‐D beams, which differ in their manifestation of the above limitation. The first has already been described in the literature and involves the interpolation of iterative rotations, while an alternative formulation, which eliminates the above effect by design, requires interpolation of incremental rotations. Theoretical arguments are backed by numerical results. Similarities between the conventional and new formulation are pointed out and are shown to be big enough to enable easy transformation of the conventional formulation into the new one. © 1998 John Wiley & Sons, Ltd.