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 C1-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 C1
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