Strong multipatch C1-coupling for isogeometric analysis on 2D and 3D domains

Abstract The solution spaces of isogoemetric analysis (IGA) constructed from p degree basis functions allow up to C p − 1 continuity within one patch. However, for a multi-patch domain, the continuity is only C 0 at the boundaries between the patches. In this study, we present the construction of basis functions of degree p ≥ 2 which are C 1 continuous across the common boundaries shared by the patches. The new basis functions are computed as a linear combination of the C 0 basis functions on the multi-patch domains. An advantage of the proposed method is that for the new basis functions, the continuity within a patch is preserved, without additional treatment of the functions in the interior of the patch. We apply continuity constraints to the new basis functions to enforce C 1 continuity, where the constraints are developed according to the concept of “matched G k -constructions always yield C k -continuous isogeometric elements” discussed in Groisser and Peters, (2015). However, for certain geometries, the over-constrained solution space will lead to C 1 locking (Collin and Sangalli, 2016). We discuss and show the usage of partial degree elevation to overcome this problem. We demonstrate the potential of the C 1 basis functions for IGA applications through several examples involving biharmonic equations.