A fully explicit isogeometric collocation formulation for the dynamics of geometrically exact beams
<|reference_start|>A fully explicit isogeometric collocation formulation for the dynamics of geometrically exact beams: We present a fully explicit dynamic formulation for geometrically exact shear-deformable beams. The starting point of this work is an existing isogeometric collocation (IGA-C) formulation which is explicit in the strict sense of the time integration algorithm, but still requires a system matrix inversion due to the use of a consistent mass matrix. Moreover, in that work, the efficiency was also limited by an iterative solution scheme needed due to the presence of a nonlinear term in the time-discretized rotational balance equation. In the present paper, we address these limitations and propose a novel fully explicit formulation able to preserve high-order accuracy in space. This is done by extending a predictor--multicorrector approach, originally proposed for standard elastodynamics, to the case of the rotational dynamics of geometrically exact beams. The procedure relies on decoupling the Neumann boundary conditions and on a rearrangement and rescaling of the mass matrix. We demonstrate that an additional gain in terms of computational cost is obtained by properly removing the angular velocity-dependent nonlinear term in the rotational balance equation without any significant loss in terms of accuracy. The high-order spatial accuracy and the improved efficiency of the proposed formulation compared to the existing one are demonstrated through some numerical experiments covering different combinations of boundary conditions.<|reference_end|>
@article{ferri2024a,
    title={A fully explicit isogeometric collocation formulation for the dynamics
  of geometrically exact beams},
    author={Giulio Ferri, Josef Kiendl, Alessandro Reali, Enzo Marino},
    journal={arXiv preprint arXiv:2408.08727},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.08727},
    primaryClass={cs.CE cs.NA math.NA}
}