
Scaled Boundary Isogeometric Analysis Combined with the Finite Cell Method for Trimming in Planar Domains
Please login to view abstract download link
Modern applications of numerical structural analysis in combination with the digitalization of objects, have triggered a tremendous growth in geometric complexity of structural components. The alignment of geometric design model and numerical model for analysis has a huge impact on the preparation of the analysis model and computation time. With the development of isogeometric analysis the gap between design and analysis was addressed. Besides, in recent years, the scaled boundary method gained more attention as it takes the boundary of an object more into account and provides the parametrization of any polygonal domain with the only requirement of starshapedness thereof. The parametrization was proven as a powerful approach in static analysis particularly for trimmed domains as shown [1] and [2]. However, if the computational domain is not starshaped, domain decomposition methods need to be taken into account to obtain starshaped subdivisions, which is especially time consuming in the design process as a single trimming curve in the interior of the domain requires a domain decomposition. Additionally, trimming can be handled by immersed boundary methods such as the finite cell method [3], CutFEM or the shifted boundary method. In the finite cell method, the physical domain is embedded into the extended fictitious domain to use a simple mesh that is not conform to the boundary of the physical domain. To account for the geometry, specialized integration schemes are employed such as adaptive integration or moment fitting. In this contribution, we present the scaled boundary isogeometric analysis for planar domains considering planar linear elasticity and Reissner-Mindlin plates. Further, the approach is combined with the finite cell method which gives the advantage of an explicitly defined boundary by incorporation potential trimming curves at the boundary directly in the model description and considering interior trimming by a finite cell approach. Besides the exact boundary description, the scaled boundary cubature can be utilized at the interior in the vicinity of the trimmed areas to have precise quadrature for the cut cell approach. The results are compared to other cut cell approaches. [1] Arioli et al. “Scaled boundary parametrizations in isogeometric analysis” [2] Reichle et al. "Smooth multi-patch scaled boundary isogeometric analysis for Kirchhoff–Love shells” [3] Rank et al. “Geometric modeling, isogeometric analysis and the finite cell method"