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2023 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 412, article id 116074Article in journal (Refereed) Published
Abstract [en]
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.
Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Critical time step, Explicit dynamics, Finite cell method, Ghost penalty, Immersogeometric analysis, Mass scaling
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-208258 (URN)10.1016/j.cma.2023.116074 (DOI)001005125000001 ()2-s2.0-85156266206 (Scopus ID)
Funder
EU, Horizon 2020, 101017578
2023-05-152023-05-152023-09-05Bibliographically approved