Gradient Based Structural Optimization of a Stringer Stiffened Composite Wing Box with Variable Stringer Orientation

Abstract

The structural optimization plays a key role in multidisciplinary optimization. The proof of structural integrity is a prerequisite for the performance assessment of a wing design. In addition, the modification of the structural design allows changing the bend-twist coupling properties in a beneficial way for overall cruise performance. Due to the high number of design variables affecting the mass and stiffness of a wing box, a gradient based process is established. It meets the needs of fast convergence and enables the coupling with aerodynamic analyses that provide gradients as well. A well suited parametrization of the design variables is necessary, especially for composite materials. Therefore, lamination parameters are used, which are proven to be suitable for gradient based optimization. In order to consider stiffening structures (i.e. stringer on the wing cover), a smeared stiffener approach is used. With this approach, it is not necessary to model the stringer explicitly in the Finite Element model. The influence of different stringer shapes and their orientation can be evaluated with the method suggested in this paper. In order to reduce calculation time, the numerical model is evaluated using analytic formulations for global and local stability as well as strength. The two approaches, smearing the stiffeners or explicitly modeling stiffeners, are validated by comparison of global deformations. The optimization process is applied to a representative wing box loaded with an eccentric load. The influence of different stringer orientations on the structural deformation is examined in conjunction with the optimization of lamination parameters.