On penalty-free formulations for multipatch isogeometric Kirchhoff–Love shells

One of the distinguishing features of Isogeometric Analysis is the usage of the same function space for describing the global, pre-discretization domain of a partial differential equation and for approximating its solution. Quite often, however, the domain consists of several patches where each patch is parametrized by means of Non-Uniform Rational B-Splines (NURBS), and these patches are then glued together by means of continuity conditions. While techniques known from domain decomposition can be carried over to this situation, the analysis of shell structures is substantially more involved as additional angle preservation constraints between the patches might arise. In this paper, we address this issue in the stationary and transient case and make use of the analogy to constrained mechanical systems with joints and springs as interconnection elements. Starting point of our work is the bending strip method (Kiendl et al., 2010) which adds extra stiffness to the interface between adjacent patches and which is found to lead to a so-called stiff mechanical system that might suffer from ill-conditioning and severe step size restrictions during time integration. As a remedy, an alternative formulation is developed that improves the condition number of the system and removes the penalty parameter dependence. Moreover, we study another alternative formulation with continuity constraints applied to triples of control points at the interface. Numerical results show a comparison between the different formulations where we observe that the alternative formulations are well conditioned, independent of any penalty parameter and give the correct results.