Design method for winding angle of composite shell based on principal stress lines

The winding angle is a key design parameter of filament-wound composite motor cases for solid rocket engines, which directly affects their load-bearing performance. Existing winding angle design methods usually rely on iterative finite element optimization, resulting in high computational cost and low design efficiency. To address this issue, this study proposes a winding angle design method based on principal stress trajectories, aiming to achieve an efficient design. First, a theoretical model was established to describe the relationship between the case characteristic coefficient and stress state, demonstrating that aligning fibers with principal stress trajectories leads to the highest material utilization and optimal load-bearing performance. Subsequently, a computational approach was developed to extract principal stress trajectories of helical winding layers from the stress tensor obtained by finite element analysis of the case. Based on the non-geodesic winding theory and under the constraint of preventing fiber slippage, a winding angle design method was formulated by minimizing the deviation between the winding path and the principal stress trajectories. Finally, finite element simulations and hydraulic burst tests were carried out to validate the proposed method. The results show that, within the limits of winding process constraints, winding paths with minimal deviation from the principal stress trajectories yield the highest burst pressure and characteristic coefficient of the case, thereby confirming the effectiveness of the proposed approach.