Critical time-step size analysis and mass scaling by ghost-penalty for immersogeometric explicit dynamics

Critical time-step size analysis and mass scaling by ghost-penalty for immersogeometric explicit dynamics

Stoter, Stein K.F. (Eindhoven University of Technology)
Divi, Sai C. (Eindhoven University of Technology)
van Brummelen, E. Harald (Eindhoven University of Technology)
Larson, Mats G. (Umeå University)
de Prenter, Frits (TU Delft Wind Energy)
Verhoosel, Clemens V. (Eindhoven University of Technology)

2023

In this article, we study the effect of small-cut elements on the critical time-step size in an immersogeometric explicit dynamics context. We analyze different formulations for second-order (membrane) and fourth-order (shell-type) equations, and derive scaling relations between the critical time-step size and the cut-element size for various types of cuts. In particular, we focus on different approaches for the weak imposition of Dirichlet conditions: by penalty enforcement and with Nitsche's method. The conventional stability requirement for Nitsche's method necessitates either a cut-size dependent penalty parameter, or an additional ghost-penalty stabilization term. Our findings show that both techniques suffer from cut-size dependent critical time-step sizes, but the addition of a ghost-penalty term to the mass matrix serves to mitigate this issue. We confirm that this form of ‘mass-scaling’ does not adversely affect error and convergence characteristics for a transient membrane example, and has the potential to increase the critical time-step size by orders of magnitude. Finally, for a prototypical simulation of a Kirchhoff–Love shell, our stabilized Nitsche formulation reduces the solution error by well over an order of magnitude compared to a penalty formulation at equal time-step size.

Critical time step
Explicit dynamics
Finite cell method
Ghost penalty
Immersogeometric analysis
Mass scaling

http://resolver.tudelft.nl/uuid:11e3394a-56a6-4065-9ea8-f64968ae2f24

https://doi.org/10.1016/j.cma.2023.116074

0045-7825

Computer Methods in Applied Mechanics and Engineering, 412

Institutional Repository

journal article

© 2023 Stein K.F. Stoter, Sai C. Divi, E. Harald van Brummelen, Mats G. Larson, Frits de Prenter, Clemens V. Verhoosel