Multi-patch isogeometric analysis for Kirchhoff–Love shell elements

We formulate a methodology to enforce interface conditions preserving higher-order continuity across the interface. Isogeometrical methods (IGA) naturally allow us to deal with equations of higher-order omitting the usage of mixed approaches. For multi-patch analysis of Kirchhoff–Love shell elements, G ¹ continuity at the interface is required and serve here as a prototypical example for a higher-order coupling conditions. When working with this class of shell elements, two different types of constraints arise: Higher-order Dirichlet conditions and higher-order patch coupling conditions. A basis modification approach is presented here, based on a least-square formulation and the incorporation of the constraints into the IGA approximation space. An alternative formulation using Lagrange multipliers which are statically condensed via a discrete Null-Space method provides additional insight into the proposed formulation. A detailed comparison with a classical mortar approach shows the similarities and differences. Eventually, numerical examples demonstrate the capabilities of the presented formulation.