Scaled boundary isogeometric analysis with C1 coupling for Kirchhoff‐Love theory

Abstract

AbstractScaled boundary isogeometric analysis (SB‐IGA) describes the computational domain by proper boundary NURBS together with a well‐defined scaling center; see [5]. More precisely, we consider star convex domains whose domain boundaries correspond to a sequence of NURBS curves and the interior is determined by a scaling of the boundary segments with respect to a chosen scaling center. However, providing a decomposition into star shaped blocks one can utilize SB‐IGA also for more general shapes. Even though several geometries can be described by a single patch, in applications frequently there appear multipatch structures. Whereas a C0 continuous patch coupling can be achieved relatively easily, the situation becomes more complicated if higher regularity is required. Consequently, a suitable coupling method is inevitably needed for analyses that require global C1 continuity.In this contribution we apply the concept of analysis‐suitable G1 parametrizations [2] to the framework of SB‐IGA for the C1 coupling of planar domains with a special consideration of the scaling center. We obtain globally C1 regular basis functions and this enables us to handle problems such as the Kirchhoff‐Love plate and shell, where smooth coupling is an issue. Furthermore, the boundary representation within SB‐IGA makes the method suitable for the concept of trimming. In particular, we see the possibility to extend the coupling procedure to study trimmed plates and shells.The approach was implemented using the GeoPDEs package [1] and its performance was tested on several numerical examples. Finally, we discuss the advantages and disadvantages of the proposed method and outline future perspectives.