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This paper presents a model for aeroelastic optimization of functionally graded, plate subsonic wings. The objective is the maximization of the critical flight speed at which wing divergence occurs, while maintaining the total structural mass at a constant value equals to that of a known baseline design. The major aim of the study is to tailor the fiber volume fraction distribution in order to improve the wing aeroelastic performance and broaden its stability boundaries without mass penalty. Various power-law mathematical expressions describing material grading along the wing span as well as the airfoil thickness directions have been utilized, where the power exponent is taken as a main design variable. The pre-assigned aerodynamic parameters are chosen to be the wing area, aspect ratio and chord taper ratio. The mathematical model employs the classical plate and beam theories for determining elastic deformations of the wing structure, and the modified strip theory for calculating the aerodynamic loads that arise from these deformations. This representation, together with the classical lamination theory, allows the solution of the wing divergence problem using the finite element method. The resulting optimization problem has been solved by invoking the MATLAB optimization Toolbox routines, which implement the sequential quadratic programming method. Adequate scaling and non-dimensionalization of the various parameters and variables are utilized in order to make the model valid for a variety of wing configurations and types of material of construction. A case study involving the optimization of a tapered plate subsonic wing made of carbon-AS4/epoxy-3501-6 composites is presented. Trends for good designs having expanded aeroelastic stability boundary under the imposed mass constraint are discussed. Results show that the approach implemented in this study can be efficient in producing improved designs in a reasonable computer time.

AEROELASTIC OPTIMIZATION OF FUNCTIONALLY GRADED WINGS