Intrinsically Selective Mass Scaling With Hierarchic Plate and Shell Formulations

  • Reinken, Lisa-Marie (University of Stuttgart)
  • Jakob, Henrik (University of Stuttgart)
  • Oesterle, Bastian (Hamburg University of Technology)
  • Bischoff, Manfred (University of Stuttgart)

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For explicit time integration schemes in structural dynamics, the size of the time steps is limited by a stability criterion. This critical time step size depends on the highest frequency of the discretized problem. Mass scaling methods, increasing the inertia, can be used to reduce these frequencies, however at the cost of compromising accuracy. For shear deformable beam, plate and shell formulations, the time step is typically limited by the highest transverse shear frequencies. In many applications, these are of minor importance for the structural response. Hierarchic formulations with a direct parametrization of variables related to transverse shear deformations allow a selective mass scaling, increasing the inertia related to transverse shear in a simple manner, while bending frequencies remain practically unaffected [1]. This novel concept of Intrinsically Selective Mass Scaling (ISMS) facilitates to increase the critical time step, while featuring high accuracy and preserving both linear and angular momentum for both consistent and lumped mass matrices. Unlike other selective mass scaling techniques, ISMS preserves the diagonal structure of lumped mass matrices. Similar to the underlying intrinsically locking-free, hierarchic concept for shear deformable structural element formulations, ISMS retains its beneficial properties for any smooth discretization scheme. This contribution explains the concept of ISMS and discusses the pros and cons of formulations relying on hierarchic rotations [2] and hierarchic displacements [3] in this context. Both frequency spectra and transient analysis with explicit time integration are investigated in numerical experiments. The performance of ISMS in comparison with state-of-the-art mass scaling is showcased for isogeometric discretizations based on B-splines. REFERENCES [1] L.-M. Krauß, R. Thierer, M. Bischoff, and B. Oesterle. Intrinsically selective mass scaling with hierarchic plate formulations. Computer Methods in Applied Mechanics and Engineering 432, (2024), https://doi.org/10.1016/j.cma.2024.117430 [2] R. Echter, B. Oesterle, M. Bischoff. A hierarchic family of isogeometric shell finite elements. Computer Methods in Applied Mechanics and Engineering 254, (2013), https://doi.org/10.1016/j.cma.2012.10.018 [3] B. Oesterle, E. Ramm, M. Bischoff. A shear deformable, rotation-free isogeometric shell formulation. Computer Methods in Applied Mechanics and Engineering 307, (2016), https://doi.org/10.1016/j.cma.2016.