Explicit dynamic isogeometric B-Rep analysis of penalty-coupled trimmed NURBS shells

Abstract

Isogeometric B-Rep Analysis (IBRA) was the first approach that enabled a full integration of Computer Aided Design (CAD) and Computer Aided Engineering (CAE) based on trimmed NURBS B-Rep models ubiquitous in industrial CAD. However, the applicability of IBRA to explicit dynamic problems such as vehicle crash simulations and especially the effect of trimming and penalty coupling on the critical time step were not systematically investigated in the literature. To fill this gap, we developed Explicit IBRA, a combination of the patch coupling capabilities of IBRA with the explicit dynamic features of the FE solver LS-DYNA.For Explicit IBRA, we particularly (i) developed a new penalty-based B-Rep element formulation for the application to a Reissner–Mindlin shell with six degrees of freedom, (ii) formally extended the IBRA theory to explicit time integration schemes, (iii) showed that the common stability criterion and the maximum eigenvalue-based time step estimation from FE still hold, and (iv) used the IBRA exchange format to implement a closed design workflow between the CAD program Rhinoceros and the solver LS-DYNA. We solved selected benchmark problems, from quasi-static linear elastic to highly dynamic elasto-plastic with large deformations, and obtained accurate results with penalty factors that cause no or only a minor decrease in stable time step size. That is, we found that penalty coupling does not have a severe impact on the critical time step in explicit analysis, making Explicit IBRA practically applicable. Finally, we studied an industrial BMW engine bonnet model under dynamic loading and observed good agreement with reference finite element simulations.