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-$C^1$, Analysis-Suitable $G^1$ and the Approximate $C^1$ 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 $C^1$ and Analysis-Suitable $G^1$ 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-$C^1$ and D-Patch provide relatively easy construction on complex geometries. The Almost-$C^1$ 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 $C^1$ and Analysis-Suitable $G^1$ applicable to more complex geometries.

翻译：为在复杂域上实现具有更高光顺性的等几何分析，可采用修剪法、变分耦合法或非结构化样条方法。后两类方法需要将域分割为多片，并在片界面处提供连续基函数。在壳建模领域，变分方法被广泛使用，而非结构化样条方法在壳问题中的应用则相对较少。本文据此对若干非结构化样条构造方法（特别是D-Patch、Almost-$C^1$、分析适用$G^1$及近似$C^1$）进行了定性与定量比较，旨在为实际问题的选型提供见解，并指出未来研究方向。在定性比较中，评估并对比了各方法的特性；在定量比较中，通过精选数值算例凸显各方法的优劣差异，并同时将其与弱耦合法（如Nitsche法或罚函数法）进行对比。简言之，结论表明：近似$C^1$与分析适用$G^1$在双调和问题分析中无需特殊细化算法即能实现最优收敛，且能提供精确的应力场；而Almost-$C^1$与D-Patch在复杂几何上构造相对简便——Unlike D-Patch, Almost-$C^1$方法对边界顶点价数无限制，但仅适用于双二次局部基函数。基于上述结论，本文提出了未来研究方向，例如推动近似$C^1$和分析适用$G^1$在更复杂几何上的适用性。