Analysis-oriented Loop control-mesh construction for Kirchhoff–Love shell IGA on trimmed NURBS surfaces

Loop subdivision provides a smooth triangular approximation space for Kirchhoff–Love shell isogeometric analysis. Current workflows commonly generate Loop control meshes during geometric preprocessing, leaving their evaluation structure outside the analysis-discretization design. For trimmed non-uniform rational B-spline (NURBS) shells, this separation can affect both computational efficiency and geometric consistency. Geometry-first meshes may distribute extraordinary vertices throughout the interior and increase irregular Loop evaluations during stiffness integration and derivative-sensitive post-processing. Uniformly weighted fitting may also leave geometry errors concentrated near trimming boundaries. This paper develops an analysis-oriented construction strategy that addresses these topology and geometry requirements jointly. A near-regular topology retains a valence-six interior and confines trimming-induced irregularity to a finite boundary layer. The control points are fitted using the strict Loop limit basis. A topology-preserving boundary-weighted variant further improves the representation of trimmed boundaries. Geometry studies on controlled trimmed surfaces, close-feature configurations, and an imported car panel show that the near-regular meshes confine extraordinary vertices to the prescribed boundary neighborhoods and that boundary weighting produces substantial boundary-region error reductions at the finer levels. At the finest star-shaped and elliptic-hole resolutions, boundary weighting reduces the boundary-layer root-mean-square (RMS) geometry error by 74%–90% relative to the uniformly weighted near-regular fit. Kirchhoff–Love shell studies with literature and conventional finite-element references show that the near-regular meshes attain the lowest errors for several global and energy-based response measures. At approximately 1 0 4 control vertices across the three application studies, the mean Delaunay-baseline times are 2.4–3.1 times the mean near-regular times for element computation and stress post-processing. These results show that analysis-oriented control-mesh construction combines competitive mechanical accuracy with substantially improved Loop evaluation efficiency. Boundary-weighted fitting provides an additional improvement in geometric consistency at trimmed boundaries.