A sensitivity-based parameterization concept for the automated design and placement of reinforcement doublers

This paper presents a sensitivity-based approach for an automated generation of laminated composite structures with local reinforcement doublers. The method is demonstrated on the problem of finding structural design solutions with maximal frequency-to-mass ratios but can be extended to optimization of different objectives. Eigenvalue sensitivities on finite element level with respect to the thickness of laminate layers are derived analytically and provide the basis for the generation of laminate doublers. Sensitivities can also be evaluated for non-existent layers, namely Ghost Layers. Predefined material properties and orientations are assigned to them but their thickness is specified to zero by a thickness control factor. Assigning a real thickness to parts of these layers, which is controlled by sensitivity information, creates local reinforcement doublers. The locally reinforced solutions are superior to solutions with fully covered layers in terms of eigenfrequency-to-mass ratio. Due to the choice of the parameterization and the iterative thickening process, solutions can be manufactured without significant modifications. The efficiency as well as the solution quality is demonstrated with a numerical experiment.