An aero-structural multi-disciplinary optimization method for 3D wing was developed using Euler equations

continuous adjoint method

FFD(free-form deformation) strategy and a linear quadrilateral shell model. The objective function is the weighted sum of drag coefficient and the structural weight of the wing box. The design variables include the control points of FFD volume and the thicknesses of ten skin segments. The gradients of lift coefficient and drag coefficient with respect to design variables were adopted by continuous adjoint method

the gradients of wing box weight were acquired directly

and the gradients of the stress were obtained with finite difference method. The aero-structural multi-disciplinary optimization method was applied to a high aspect ratio wing in transonic regime

and a comparison between the results from aero-structural analysis of single-disciplinary optimization and aero-structural optimization was presented. It showed that the drag coefficient and the weight can decrease simultaneously through aero-structural optimization while the constraints were satisfied to keep the results reasonable.