This paper proposes a novel framework for constructing C1 smooth isogeometric functions on the planar multipatch domain. We extend the concept of C1 coupling, wherein the null space approach was used to construct geometrically continuous basis functions as linear combinations of C0 basis functions near patch junctions. However, due to the lack of continuity constraints, the resulting approximate basis functions violated the partition of unity and non-negativity properties. The proposed framework enforces the partition of unity and non-negativity conditions through additional equations, preserving higher-order continuity across the interface. The patch coupling algorithm provided generates C1 smooth isogeometric functions for arbitrarily shaped planar multipatch geometries. The advantage of this proposed approach is a reduced degree of approximation and a smooth transition from 1D to 2D patch coupling methodology. The computational effort to determine a new set of basis functions is significantly reduced due to the partition of unity property. Numerical studies are performed for the Kirchhoff–Love plate and biharmonic equations on various curved multipatch geometries, including an additional patch test. Enhanced numerical accuracy is observed for geometries with curved interfaces and boundaries. The accuracy and numerical efficiency of the proposed framework are analysed through L2 and H02 errors, showing optimal convergence behaviour for different polynomial orders. Furthermore, well-conditioned global matrices are observed with increasing refinement levels, demonstrating the efficiency of the methodology.

中文翻译：

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为基于 NURBS 的分析开发用于平面多面体域的 [公式省略] 平滑等几何函数


本文提出了一种新的框架，用于在平面多面体域上构建 C1 平滑等几何函数。我们扩展了 C1 耦合的概念，其中零空间方法用于将几何连续基函数构造为贴片连接附近 C0 基函数的线性组合。然而，由于缺乏连续性约束，得到的近似基函数违反了单位和非负性质的划分。所提出的框架通过附加方程强制划分单位和非负性条件，从而保持整个界面的高阶连续性。提供的面片耦合算法为任意形状的平面多面体几何生成 C1 平滑等几何函数。这种提出的方法的优点是降低了近似度，并且从 1D 到 2D 补丁耦合方法的平滑过渡。由于 unity 属性的分区，确定一组新基函数的计算工作量显著减少。对 Kirchhoff-Love 板和双谐波方程在各种弯曲的多面体几何形状上进行了数值研究，包括额外的斑贴试验。对于具有弯曲界面和边界的几何结构，可以观察到更高的数值精度。通过 L2 和 H02 误差分析了所提出的框架的准确性和数值效率，显示了不同多项式阶次的最佳收敛行为。此外，观察到条件良好的全局矩阵，细化水平不断提高，证明了该方法的有效性。