Critical Time Step Analysis for Trimmed B-Splines, LR-Splines, and THB-Splines in Explicit Dynamics

  • Hollweck, Christoph (TU München/ OTH Regensburg)
  • Leidinger, Lukas (ANSYS)
  • Hartmann, Stefan (ANSYS)
  • Wagner, Marcus (OTH Regensburg)
  • Wüchner, Roland (TU München)

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Isogeometric Analysis (IGA) has gained attention due to its superior numerical properties and its potential to streamline the transition from CAD to analysis. When integrated with the concept of trimming, IGA offers significant potential for large-scale industrial explicit dynamics, such as vehicle crashworthiness and sheet-metal forming simulations. However, since explicit schemes are conditionally stable, understanding the behavior of the critical time step under arbitrary trimming configurations is crucial for industrial viability. This work extends previous investigations on the critical time step of trimmed B-splines to LR-splines and THB-splines. Through the analysis of 1D and 2D models, we identify that refined boundary elements in open knot vectors act as the primary bottleneck for the stable time step. While trimming these boundary elements generally increases the critical time step, we show that specific configurations, such as narrow ribs, introduce new restrictions. Furthermore, we reveal that even under favorable trimming conditions, spectral outliers emerge at the high end of the eigenfrequency spectrum, limiting the overall time step. To address these limitations, we propose the Indirect Boundary Coarsening (IBC) method. By utilizing local refinement exclusively in the interior while keeping trimmed basis functions unrefined, IBC effectively increases the critical time step beyond the limits of standard B-splines of comparable element size. Our results demonstrate that while LR- and THB-splines generally impose constraints equivalent to standard B-splines, they offer significantly larger stable time steps when combined with the IBC method. The practical feasibility of this approach is validated through nonlinear sheet-metal forming simulations in LS-DYNA. This study represents the first industrial application of trimmed, locally refined isogeometric shells in a complex explicit workflow, proving their potential for large-scale engineering applications.