Three-stage integrated optimization of topology and fiber path for variable-stiffness composite laminates

The integrated optimization of topology and fiber path in variable-stiffness composite laminates (VSCL) poses significant challenges due to the inherent strong non-convexity. To address these issues, this paper proposes a novel three-stage integrated optimization framework. In the first stage, lamination parameters are selected as the intermediate variables to overcome the local optima behaviors derived from directly optimizing fiber angles. The Kreisselmeier-Steinhauser (KS) function aggregation strategy is employed to efficiently handle the feasible domain constraints of the lamination parameters. The optimal lamination parameter distribution and topology shape are obtained simultaneously. The second stage aims to retrieve the fiber angles from the optimal lamination parameters. An inverse model based on least-squares error minimization is established, followed by the Improved Direct Simulated Annealing (IDSA) algorithm for parallel discrete fiber angle search. In the third stage, a continuous fiber angle correction model is established, with the discrete fiber angles obtained in the previous stage taken as the initial solution. The continuous fiber angle distribution matching the optimal topological configuration is obtained. Subsequently, a curved fiber path fitting method is introduced to transform the continuous fiber angles into manufacturable paths that are continuous, equally spaced, and free of intersecting. Numerical examples demonstrate that the proposed framework achieves high-performance design for VSCL, while ensuring good convergence and robust global optimization capability.