Mixed-integer, multi-objective layerwise optimization of variable-stiffness composites with gaps and overlaps

Automated fiber placement (AFP) has made it possible to vary the steering angle along curvilinear fiber paths, thus improving mechanical performance compared to traditional composite materials. Variable-angle tow (VAT) or variable-stiffness composites (VSC) have been developed to enhance structural performance through material optimization and effective load-bearing configurations. These advanced materials contribute to achieving optimal performance while reducing the weight of aircraft and aerospace structures. However, defects such as gaps and overlaps may arise during the manufacturing process. Whereas the latter increases local thickness, the former causes resin-rich areas within each lamina. The mass and structural optimization of this kind of structure is challenging as it combines discrete and continuous design variables, namely the number of layers and the fiber path parameters, where the latter influence the presence of defects within the laminate. To tackle this optimization problem, this work proposes a mixed-integer strategy specifically designed to select the least-weight design of a VAT laminate while also fulfilling requirements on the first natural frequency and buckling load while accounting for the manufacturing signature of the AFP process. This study combines the Carrera unified formulation (CUF) and the defect layer method (DLM) to model the VAT laminates and incorporating the fabrication defects. The research has two main aims: (i) to determine the minimum number of layers required to satisfy the fundamental frequency and buckling constraints, considering the manufacturing signature, and (ii) to investigate the influence of the selected structural theory on the optimal design solutions.