Prof. Dr. Dietmar Hömberg

Scientist in Charge of Application Field Sustainable Energies

Weierstrass-Institut für Angewandte Analysis und Stochastik
Mohrenstr. 39
10117 Berlin
+49 (0) 30 20372 491

Projects as a project leader

  • SE13

    Topology optimization of wind turbines under uncertainties

    Dr. Martin Eigel / PD Dr. René Henrion / Prof. Dr. Dietmar Hömberg / Prof. Dr. Reinhold Schneider

    Project heads: Dr. Martin Eigel / PD Dr. René Henrion / Prof. Dr. Dietmar Hömberg / Prof. Dr. Reinhold Schneider
    Project members: Dr. Johannes Neumann / Dr. Thomas Petzold
    Duration: -
    Status: completed
    Located at: Technische Universität Berlin / Weierstraß-Institut


    The application focus of this project is the topology optimization of the main frame of wind turbines. This is the central assembly platform at the tower head accommodating the drive train, the generator carrier, the azimuth bearing and drives and a lot of small components. Topology optimization should not be mistaken for legally mandated structural analysis computations. For the latter, it is standard to solicit a number of single load scenarios based on available time series data. While this approach is questionable already for stress analysis, it is prohibitive for topology optimization. Disregarding the multivariate distribution of the random loads would not provide any probabilistic certificate for bounding stresses. Moreover, the natural way to choose weights is to derive a stochastic load from available time series data. The main frame is made of cast iron which is prone to a number of material impurities like shrink holes, dross, and chunky graphite. This motivates the additional consideration of randomness for the material stiffness. Structures resulting from topology optimization often exhibit unacceptably high stresses necessitating costly subsequent shape design works. To avoid this already during the optimization, state constraints have to be included in the optimization problem. The main novelty of this project is that it combines a phase field relaxed topology optimisation problem not only with uncertain loading and material data but also with chance state constraints. Even in the finite-dimensional case, the derivation of optimality conditions including gradient formulas is completely open. In the long run, including an appropriate damage model as additional state equation will be a further task of great practical importance.