Simultaneous topology and fiber path optimization for variable stiffness Double-Double laminates with strength control

Variable stiffness laminates offer the advantage of tailoring structural performance by adjusting in-plane stiffness through curved fiber paths. Additionally, material distribution at the structural level can further fine-tune performance by varying the topology. If both the structural topology and curved fiber paths are optimized together, super-efficient composite laminates can be achieved. In this paper, a simultaneous topology and fiber path optimization method based on a coarse background mesh is proposed for variable stiffness Double-Double (DD) laminates with strength control. Firstly, elemental pseudo densities and nodal fiber orientations are selected as design variables to control topology and curved fiber paths, respectively. Due to the reduced design redundancy in DD laminates, only two independent fiber orientations are necessary for each node of a coarse background mesh. This ensures global fiber path continuity through interpolation of elemental values. Additionally, it helps decouple fiber path generation from the computationally expensive finite element analysis, significantly reducing the number of design variables and related constraints. Secondly, an optimization model is developed to maximize the laminate strength while satisfying weight and compliance constraints. The nested p-norm of Tsai-Hill failure indices is used to aggregate stresses across different elements and layers, enhancing the overall calculation efficiency. Additionally, minimum angle difference constraints are incorporated between the two groups of DD angles to ensure the laminate’s ability to resist secondary loads, thereby improving structural integrity. Notably, the proposed framework is the first to address the simultaneous optimization of both topology and curved fiber paths with strength considerations for multi-layer composite laminates. Sensitivities for both topology and fiber orientation design variables are efficiently calculated by solving a single adjoint problem, significantly improving computational efficiency. Finally, representative numerical examples demonstrate the effectiveness of the proposed method, achieving significant stress concentration reductions (over 40 %) compared to results from topology optimization alone. The optimized designs exhibit more compact topologies, improved load transfer, and enhanced resistance to secondary loading, validating the robustness of the proposed method.