Shape Optimization for Natural Frequency with Isogeometric Kirchhoff-Love Shell and Sensitivity Mapping

A fast shape optimization strategy for free form shell structure design with structural dynamics criteria is proposed in this paper. The structures are modelled with Non-Uniform Rational B-Spline based isogeometric Kirchhoff-Love shell elements. The substitution of the traditional finite elements not only makes the mesh model geometrically exact but also avoids the laborious mesh regeneration during the design update. As for the structural response evaluation, the modal synthesis method is adopted to avoid a repeated evaluation of some substructures where there are no designed variables attached; thus, the model reanalysis is speeded up. A bottom-up strategy for the analytical design sensitivity evaluation is also proposed here; the element-level analytical sensitivity with respect to the inherent shape parameters is firstly calculated from which the design sensitivity is then extracted with the help of a sensitivity map. Finally, gradient based algorithm is used to solve the optimization problem. Several examples show that our approach is flexible and efficient for fast free form shell structure optimization.