Advanced Isogeometric Design-through-analysis Concepts

The central result of the my doctoral project is an isogeometric design-through-analysis methodology for three-dimensional solid structures described by T-spline CAD surfaces. It achieves all key benefits of isogeometric analysis, such as a seamless integration of the CAD geometry, no expensive mesh generation, and the use of smooth higher-order B-splines for the approximation of solution fields. The proposed project extends the present state of development by two important aspects: First, modern preconditioning techniques for strongly ill-conditioned systems of equations are studied to identify a suitable way to make the present approach accessible to efficient and easy-to-parallelize iterative solvers. Second, the isogeometric design-through-analysis methodology is combined with direct im-plicit time integration schemes for the solution of transient problems of structural dynamics. In addition, research is extended beyond my doctoral work to further advanced isogeometric concepts, in particular to isogeometric collocation and T-splines. The proposed project is carried out in collaboration with the group of Prof. Thomas J. R. Hughes at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin. It continues the successful collaboration, which was initiated during my doctoral work at TUM, including a previous three month visit at ICES in summer 2011. With this proposal, I would like to apply for financial support for 6 months from June to November 2012