In contrast to conventional mechanisms, compliant mechanisms exploit structural flexibility to produce controllable large deformations. Belt-rib airfoils are shape-adaptable lightweight structures based on this idea. A belt-rib structure originally consists of a deformable closed shell (belt) whose kinematic degrees of freedom are constrained by inner stiffeners called spokes. Using standard spoke elements, the possible profile changes of the airfoil are limited. The purpose of the work reported in the current article is to define an inner stiffening structure based on numerical topology optimization in order to realize arbitrary profile changes. A ground structure with moveable connection points within the external belt represents the set of possible topologies and shapes. A new modal objective function for the synthesis of compliant mechanisms with selective compliance is introduced. The optimization problem is approached by using genetic algorithms. The applicability of the current procedure is validated by a profile shape adaptation example. For this purpose, an initial profile shape and a target profile shape are defined. The outcome of the procedure is a complex inner stiffening structure, which fulfils the imposed requirements. The solution is validated by modal analysis based on an finite-element model. Furthermore, the structural behaviour is experimentally investigated.
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