Structural optimization and layout of interactive structures is an increasingly complicated task which cannot be tackled by traditional methods or experience. Capturing transition and interfacing models seriously limits the scope of state-of-the-art approaches. The major challenge is the linkage of all the involved physical models through geometry and the transformation of this information to the analysis and design models, and would be useful with models where a “translation” of geometry to, for example, a finite element setting is not required. This line of thought is the central idea for the isogeometric analysis method recently proposed by T. Hughes et. al. Here, CAD and finite element models are merged on the basis of common NURBS spaces for geometry as well as deformation. This method shows significant advantages compared to standard techniques concerning stability, accuracy and convergence.
The actual project has been working to extend this method to handle also design optimization with special focus to the shape optimal design of shell and membrane structures. On this line, as the first essential step, a fully geometrically non-linear isogeometric shell element on the basis of the Kirchhoff-shell theory has been developed and successfully established. As novel results on their own this element is formulated in terms of displacement degrees of freedom only and special means have been developed to treat geometrical continuity between multipatches in a weak form. The knot refinement strategies have been further developed to generate geometrically consistent models of different coarseness as it is necessary to distinguish between design and analysis models. Furthermore, the element has been successfully applied for the analysis of fluid-structure interaction of rotating wind turbine blades. First applications for structural shape optimization of isogeometric shells have successfully been conducted. The basis is laid for further extensions towards the shape optimization in the fully coupled, time variant regime considering.
The team structure has been designed with respect to the broad interdisciplinary aspects of the project, as there are the groups from Lehrstuhl für Statik, Technische Universität München (Prof. Bletz-inger, Dr. Wüchner, structural analysis, shape optimization, shell finite elements) and Danish Technical University (Profs. M. Bendsøe and O. Sigmund, structural optimization) defining the initial layout complemented by EADS as the industrial partner working in the field of structural optimization and analysis of aerospace structures. In a later stage the group of Prof.Y. Bazilevs, University of California at San Diego (isogeometric analysis, computational fluid dynamics and coupling) joined. Although not planned initially this connection appeared to be a great enhancement of the project regarding the basics of isogeometric analysis and towards coupled fluid-structure simulation in general and of wind turbine blades, in particular.