In order to perform isogeometric analysis with increased smoothness on
complex domains, trimming, variational coupling or unstructured spline methods
can be used. The latter two classes of methods require a multi-patch
segmentation of the domain, and provide continuous bases along patch
interfaces. In the context of shell modeling, variational methods are widely
used, whereas the application of unstructured spline methods on shell problems
is rather scarce. In this paper, we therefore provide a qualitative and a
quantitative comparison of a selection of unstructured spline constructions, in
particular the D-Patch, Almost-C1, Analysis-Suitable G1 and the
Approximate C1 constructions. Using this comparison, we aim to provide
insight into the selection of methods for practical problems, as well as
directions for future research. In the qualitative comparison, the properties
of each method are evaluated and compared. In the quantitative comparison, a
selection of numerical examples is used to highlight different advantages and
disadvantages of each method. In the latter, comparison with weak coupling
methods such as Nitsche's method or penalty methods is made as well. In brief,
it is concluded that the Approximate C1 and Analysis-Suitable G1 converge
optimally in the analysis of a bi-harmonic problem, without the need of special
refinement procedures. Furthermore, these methods provide accurate stress
fields. On the other hand, the Almost-C1 and D-Patch provide relatively easy
construction on complex geometries. The Almost-C1 method does not have
limitations on the valence of boundary vertices, unlike the D-Patch, but is
only applicable to biquadratic local bases. Following from these conclusions,
future research directions are proposed, for example towards making the
Approximate C1 and Analysis-Suitable G1 applicable to more complex
geometries