This paper presents the application of triangle configuration B-splines (TCB-splines) for representing and analyzing the Kirchhoff-Love shell in the context of isogeometric analysis (IGA). The Kirchhoff-Love shell formulation requires global $C^1$-continuous basis functions. The nonuniform rational B-spline (NURBS)-based IGA has been extensively used for developing Kirchhoff-Love shell elements. However, shells with complex geometries inevitably need multiple patches and trimming techniques, where stitching patches with high continuity is a challenge. On the other hand, due to their unstructured nature, TCB-splines can accommodate general polygonal domains, have local refinement, and are flexible to model complex geometries with $C^1$ continuity, which naturally fit into the Kirchhoff-Love shell formulation with complex geometries. Therefore, we propose to use TCB-splines as basis functions for geometric representation and solution approximation. We apply our method to both linear and nonlinear benchmark shell problems, where the accuracy and robustness are validated. The applicability of the proposed approach to shell analysis is further exemplified by performing geometrically nonlinear Kirchhoff-Love shell simulations of a pipe junction and a front bumper represented by a single patch of TCB-splines.

翻译：本文提出了在等几何分析（IGA）框架下应用三角形配置B样条（TCB-splines）来表征和分析Kirchhoff-Love壳。Kirchhoff-Love壳的公式需要全局$C^1$连续基函数。基于非均匀有理B样条（NURBS）的IGA已被广泛用于开发Kirchhoff-Love壳单元。然而，对于具有复杂几何形状的壳，不可避免地需要多个曲面片和修整技术，其中以高连续性拼接曲面片是一项挑战。另一方面，由于其非结构化特性，TCB-splines能够适应一般多边形域、支持局部细化并灵活建模具有$C^1$连续性的复杂几何形状，这自然适用于含有复杂几何的Kirchhoff-Love壳公式。因此，我们提出使用TCB-splines作为几何表示和解逼近的基函数。我们将所提方法应用于线性和非线性基准壳问题，验证了其精度和鲁棒性。通过对由单一TCB-splines曲面片表示的管接头和前保险杠进行几何非线性Kirchhoff-Love壳仿真，进一步展示了所提方法在壳分析中的适用性。