Coupling of non-conforming trimmed isogeometric Kirchhoff–Love shells via a projected super-penalty approach

Abstract

Penalty methods have proven to be particularly effective for achieving the required C1-continuity in the context of multi-patch isogeometric Kirchhoff–Love shells. Due to their conceptual simplicity, these algorithms are readily applicable to the displacement and rotational coupling of trimmed, non-conforming surfaces. However, the accuracy of the resulting solution depends heavily on the choice of penalty parameters. Furthermore, the selection of these coefficients is generally problem-dependent and is based on a heuristic approach. Moreover, developing a penalty-like procedure that avoids interface locking while retaining optimal accuracy is still an open question. This work focuses on these challenges. In particular, we devise a penalty-like strategy based on the L2-projection of displacement and rotational coupling terms onto a degree-reduced spline space defined on the corresponding interface. Additionally, the penalty factors are completely defined by the problem setup and are constructed to ensure optimality of the method. This method is particularly suited for spline spaces of moderate degrees p=2,3, where the projection is computationally efficient and the condition number related to our choice of parameters does not yield a significant deterioration of the solution accuracy. To demonstrate this, we assess the performance of the proposed numerical framework on a series of non-trimmed and trimmed multi-patch benchmarks discretized by non-conforming meshes. We remark that only water-tight geometries have been considered in this work. We systematically observe a significant gain of accuracy per degree-of-freedom and no interface locking phenomena compared to other penalty-like approaches. Lastly, we perform a static shell analysis of a complex engineering structure, namely the blade of a wind turbine.