IGA2025

Intrinsically selective mass scaling for explicit dynamic isogeometric shell analysis

  • Krauß, Lisa-Marie (University of Stuttgart)
  • Thierer, Rebecca (University of Stuttgart)
  • Bischoff, Manfred (University of Stuttgart)
  • Oesterle, Bastian (Hamburg University of Technology)

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For explicit time integration schemes in structural dynamics, the 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, which generally comes 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, which are often of minor importance for the structural response. Direct parametrization using transverse shear parameters within primal hierarchic structural element formulations [1, 2] allows a selective scaling of transverse shear frequencies in a simple manner, while bending and membrane frequencies are practically not affected. The novel concept of intrinsically selective mass scaling (ISMS) [3, 4] preserves both linear and angular momentum for both consistent and lumped mass matrices and features high accuracy. Unlike other selective mass scaling techniques, ISMS preserves the diagonal structure of lumped mass matrices. In this contribution, we present recent research on ISMS for hierarchic isogeometric plate and shell formulations. Both frequency spectra and transient analyses with explicit time integration are investigated in a set of numerical experiments. REFERENCES [1] R. Echter, B. Oesterle and M. Bischoff, A hierarchic family of isogeometric shell finite elements. Comput. Methods Appl. Mech. Engrg., Vol. 254. pp. 170–180, 2013. [2] B. Oesterle, R. Sachse and E. Ramm and M. Bischoff, Hierarchic isogeometric large rotation shell elements including linearized transverse shear parametrization. Comput. Methods Appl. Mech. Engrg., Vol. 321, pp. 383-405, 2017. [3] B. Oesterle, J. Trippmacher, A. Tkachuk, and M. Bischoff, Intrinsically selective mass scaling with hierarchic structural element formulations. Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference, pp. 99-108, 2021. [4] L.-M. Krauß, R. Thierer, M. Bischoff and B. Oesterle, Intrinsically selective mass scaling with hierarchic plate elements. Comput. Methods Appl. Mech. Engrg., Vol. 432, 117430, 2024.