Abstract:
This study investigates the draping simulation of plain-woven fabrics over multi-patch NURBS surfaces and proposes an integrated optimization framework that simultaneously constrains the maximum shear angle and the number of cut patches. First, an improved deformation-energy-based fishnet algorithm is developed, where a biquadratic Bézier mapping replaces the conventional bilinear mapping to increase the degrees of freedom for surface fitting. In the spherical-shell benchmark, the mean squared error (MSE) between the predicted shear-angle distribution and the reference solution is reduced from
0.7615 to 0.0467. To overcome the incomplete coverage commonly observed in traditional fishnet approaches on single curved surfaces, a boundary expansion strategy is introduced, in which geodesics are recursively extended to generate meshes over residual subregions, thereby eliminating draping blind zones caused by limited geodesic extend ability. Second, a global parameterization method for multi-patch NURBS assemblies is proposed. By employing a bilinear mapping, the independent parametric domains of individual patches are unified into a global 0,1×0,1 parametric space, enabling continuous mesh generation across patch interfaces. The proposed method is further validated through comparative studies against alternative algorithms and commercial software, demonstrating its accuracy and robustness. Third, to satisfy practical requirements on shear-angle limitations, a Voronoi-diagram-based parametric-domain partitioning scheme is presented, where seed locations control the partition boundaries. A genetic algorithm is then used to optimize the initial draping parameters within each subregion; in a representative cut-pattern optimization case, the maximum shear angle is reduced from an initially over-limit value of 46.29° to 22.16°. Overall, the proposed approach enables reliable draping simulation on multi-patch NURBS surfaces and provides practical support for plain-woven preform manufacturing and draping-process optimization.