Buckling Analysis and Optimization of Stiffened Variable Angle Tow Laminates with a Cutout Considering Manufacturing Constraints

Abstract

Variable angle tow laminates (VAT) and stiffeners are known to redistribute the in-plane load distribution and tailor the buckling mode shapes, respectively, for improving structural performance. To leverage the benefits of using VAT laminates in the practical applications, in the present paper, we discuss buckling load maximization conducted for a stiffened VAT laminated plate with a central cutout considering VAT laminate manufacturing constraints. Three representative boundary conditions as seen in the aerospace structures are considered: in-plane axial displacement, in-plane pure shear, and in-plane pure bending displacements. Two common manufacturing constraints, the one on the automatic fiber placement (AFP) manufacturing head turning radius and the other on the tow gap/overlap, while fabricating VAT laminates are considered in the laminate design. These two manufacturing constraints are modeled by controlling the fiber path radius of curvature and tape parallelism in optimizing the fiber path orientations for the VAT laminates. Stiffener layout and fiber path angle for the VAT laminated plates are both considered in the buckling load maximization study. To avoid using a fine mesh in modeling the stiffened VAT laminates with a cutout when employing the finite element analysis during the optimization, the VAT laminated plate and the stiffeners are modeled independently. The displacement compatibility is enforced at the stiffener–plate interfaces to ensure that the stiffeners move with the plate. Particle swarm optimization is used as the optimization algorithm for the buckling load maximization study. Optimization results show that, without considering AFP manufacturing constraints, the VAT laminates can increase the buckling loads by 21.2% and 12.4%, respectively, comparing to the commonly used quasi-isotropic laminates and traditionally straight fiber path laminates for the structure under the in-plane axial displacement case, 19.7% and 12.5%, respectively, for the in-plane shear displacement case, and 62.1% and 26.6%, respectively, for the in-plane bending displacement case. The AFP manufacturing constraints are found to have different impacts on the buckling responses for the VAT laminates, which cause the maximum buckling load to be 9.3–10.1%, 3.0–3.2%, and 23.2–29.8% less than those obtained without considering AFP manufacturing constraints, respectively, for the present studied model under in-plane axial, shear, and bending displacements.