Robust lay-down angle computation for non-geodesic filament winding of composite pressure vessels

Non-geodesic filament winding provides greater design freedom for composite pressure vessels by allowing fiber paths to deviate from geodesic directions within admissible anti-slip limits. However, after the trajectory parameters and delivery-nozzle kinematic constraints are determined, the lay-down angle must satisfy a highly nonlinear control equation and is generally unavailable in analytical form. This paper formulates lay-down angle computation as a parameterized single-variable nonlinear root-finding problem at axial nodes. Independent global scanning can provide reliable solutions at the axial nodes, but it repeatedly searches a large angular interval at each node and therefore causes redundant function evaluations. Pseudo-arclength continuation can exploit solution continuity, but when its traced path is interpolated onto the axial nodes, its solve success rate and computational cost are still affected by the continuation step-size setting. To address these issues, this paper proposes a node-oriented Propagation-Rollback Strategy (PRS) algorithm, which constructs candidate solutions using the previously accepted solution and the current geometric information, and obtains a valid solution at the current node through residual-threshold checking, protected correction, local solving, and event-triggered rollback. Numerical results show that PRS substantially reduces the average number of function evaluations compared with independent global scanning while maintaining complete Effective Coverage and low accepted residuals. Compared with the PALC baseline under the tested step-size settings, PRS achieves a higher solve success rate at the axial nodes with lower function-evaluation cost in the tested cases. These results indicate that PRS provides a stable and efficient solving algorithm at the axial nodes for lay-down angle computation in non-geodesic filament winding.