A fully explicit formulation for the dynamics of geometrically exact beams
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We present a fully explicit IGA-C formulation for the dynamics of geometrically exact beams. The IGA-C method was proposed with the aim of keeping the computational attributes of isogeometric analysis (IGA) and, at the same time, circumventing the issues related to numerical quadrature of Galerkin IGA. Since IGA-C requires only one evaluation per degree of freedom, the method is very attractive for applications where efficiency is the main goal, such as explicit dynamics. In this regard, a first explicit dynamics IGA-C formulation for the geometrically exact beams dynamics was proposed in [1]. The formulation was explicit in the sense of the time integration algorithm. The mass/inertia matrix was still consistent and a linearization of the angular acceleration was needed at each time step. In the present work, we address these two problems. In particular, we i) extend the predictor-multicorrector approach proposed in [2, 3] to the case of Timoshenko beams to avoid accuracy deterioration that would occur with standard lumping procedures; ii) propose a linear form of the time-discretized equations to avoid iterations at each time step. Robustness, computational efficiency and high-order space accuracy of the proposed formulation are shown through a number of numerical tests.
