Bilevel Programming Weight Minimization of Composite Flying-Wing Aircraft with Curvilinear Spars and Ribs

This paper studies weight minimization of a composite flying-wing aircraft using bioinspired arbitrarily shaped spars and ribs, known as SpaRibs, for the internal structural layout design. A generalized mathematical model is developed to parameterize the shape of SpaRibs using a four-node nonuniform rational basis spline curve. Additionally, for reducing weight, composite structures and lift redistribution using multiple control surfaces are considered. A stacking sequence table is used to parameterize the wing laminate configuration with ply drops for flexible wing design. For the optimization problem including topology as well as discrete and size design variables, a bilevel programming optimization is employed by using a previously developed parallel particle swarm optimization and a gradient-based optimization, respectively, for the upper- and lower-level optimization problems. The upper-level optimization problem is employed to satisfy such design requirements as the flutter constraints for achieving a specific body freedom flutter mode. The lower-level optimization is used to optimize the control surface rotations to minimize the wing root bending moment, which is considered to be a surrogate for wing weight. Different internal structural layouts and flutter constraints are studied for comparison. Optimization studies show that using SpaRibs for aircraft wing box internal structural layout design can reduce the wing weight by 21.8% as compared to the base model and by 7.3% as compared to the wing box with traditional straight spars and ribs. The additional specific flutter result constraints lead to a 4.2% increase in the wing weight for aircraft design with SpaRibs as compared to the one obtained only with the lower bound on the flutter speed.