engleski

Objective fixed-pole approach in geometrically exact 3D beams: implementational aspects

The 6D representation of the configuration tensor was used to develop a geometrically non- linear beam finite element of an arbitrary order with Lagrangian (additive) interpolation of the configurational parameters. Analogously to the 3D case, where additive interpolation of the rotational parameters results in non- objective formulation, as shown by Crisfield and Jelenić, the proposed elements exhibit even worse non-objective behaviour, evident even in planar cases! A remedy for this problem was to develop and implement the so-called generalised shape functions (given by Jelenić and Crisfield for a 3D case) for the configurational parameter (which is a 6D vector). This successfully solved the problem of objectivity, but decreased formulation robustness significantly. We assume that the cause of this are not the shape functions themselves, but the significant numerical instability of the transformational matrices they contain. In this paper we pinpoint the terms in those matrices which we assume to be responsible for loss of robustness and analyse them with respect to computational precision and propose a remedy.

3D beams ; objectivity of strain measures ; fixed-pole approach ; numerical stability

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