The paper addresses the simulation of turbulent wind gusts hitting rigid and flexible structures. The purpose is to show that such kind of complex fluid-structure interaction (FSI) problems can be simulated by high-fidelity numerical techniques with reasonable computational effort. The main ingredients required for this objective are an efficient method to inject wind gusts within the computational domain by the application of a recently developed source-term formulation, an equally effective method to prescribe the incoming turbulent flow and last but not least a reliable FSI simulation methodology to predict coupled problems based on a partitioned solution approach combining an LES fluid solver with a FEM/IGA solver for the structure. The present application is concerned with a rigid and a membranous hemisphere installed in a turbulent boundary layer and impacted by wind gusts of different strength. The methodology suggested allows to inject the gusts in close vicinity of the object of interest, which is typically well resolved. Therefore, the launch and transport of the wind gust can be realized without visible numerical dissipation and without large computational effort. The effect of the gusts on the flow field, the resulting forces on the structure and the corresponding deformations in case of the flexible structure are analyzed in detail. A comparison between the rigid and the flexible case makes it possible to work out the direct reaction of the deformations on the force histories during the impact. Furthermore, in case of the flexible structure the temporal relationships between local or global force developments and the local deformations are evaluated. Such predictions pinpoint the areas of high stresses and strains, where the material is susceptible to failure.