Topology optimization of 3D linkages with application to morphing winglets

Abstract

Topology optimization is the process of optimizing both the material layout and the connectivity inside a design domain. The first paper on topology optimization dates back to 1904, when the Australian inventor Michell derived optimality criteria for minimum weight truss structures. In 1988 Bendsøe and Kikuchi published the pioneering paper "Homogenization approach to topology optimization", laying the foundation of numerical optimization methods for topology optimization. Since then, extensive research has been performed both in academia and industry trying to solve different topology optimization problems. Due to its general applicability, topology optimization has been applied to the design of many morphing aircraft structures including morphing leading edges, trailing edges, or both. It has also been applied to complete morphing wings. Morphing structures have the ability to change their shape throughout the flight. This allows for possible weight savings and/or drag reduction, resulting in a reduced fuel consumption. Despite the great interest in morphing winglets from both Airbus and Boeing, topology optimization has not yet been used to design morphing winglets, except for previous work done by E. Gillebaart and R. De Breuker. This thesis continues with the research by focusing on the following research objective: "Developing a software tool to design amechanism for morphing winglets, using ground-structure based topology optimization, by improving, extending, and expanding the previous 2D inhouse tool." The research in this thesis is based on previous work done by the faculty. The previous 2D tool is improved, its capabilities are extended and the tool is expanded to 3D. The current tool effectively demonstrates how topology optimization, based on the ground-structure approach, can be used to obtainmechanisms for morphing winglets. A two step optimization strategy is formulated, where the mechanism is designed in the first step and sized to obtain minimum weight in the second step. Both optimizations are done using the globally convergent method of moving asymptotes (GCMMA) optimizer, combined with the adjoint sensitivity technique. Due to the large rotations of the winglet, geometric non-linearity is taken into account using the Green-Lagrange strain measure. Various mechanisms for morphing winglets were successfully designed and sized both in 2D and in 3D. In 2D mechanisms were found where the cant angle could be regulated, in 3D mechanisms were found where both the cant angle and the toe angle could be regulated. An aerodynamic load case of 5 [kN] was defined. In 2D half of this loading was assumed to act on the mechanism, resulting in a minimum weight of 15.0 [kg]. In 3D the minimum weight was found to be 48.0 [kg].