Phase-field approaches to structural topology optimization

The mean compliance minimization in structural topology optimization is solved with the help of a phase field approach. Two steepest descent approaches based on L2- and H-1 gradient flow dynamics are discussed. The resulting flows are given by Allen-Cahn and Cahn-Hilliard type dynamics coupled to a linear elasticity system. We finally compare numerical results obtained from the two different approaches

Simulation von Offshore Wind Tubinen durch computergestützte Multi-Physik

Presently there are quite a few projects in various stages of planning and construction which aim at placing wind turbines offshore for electricity generation. There the usually higher wind speeds can be exploited, but the turbines are also additionally subjected to the offshore environment, i.e. especially wave loading. Fatigue calculations of wind turbine structures usually involve Monte Carlo Simulations of their operation in turbulent wind. In the offshore environment, we have to consider a coupled system, consisting of the structure, foundation, surrounding soil, the aerodynamic system for the wind model and the hydrodynamic system for the wave model. In this work, the models have been developed initially separately and are consistently coupled here to give the whole system. They consist of: ˆ The structural subsystem, which is a nonlinear large displacement finite element model (FEM). ˆ The aerodynamic subsystem, with prescribed stochastic wind characteristics and an instationary dynamic stall model for the aeroelastic blade loading ˆ The hydrodynamic subsystem, modelled mainly as potential flow and coupled to the stochastic wave field to describe the real sea state and take the far–field into account. The computations on this part is based on the boundary element method (BEM), to make the computations faster in this part the fast multipole method is used. ˆ The soil dynamic subsystem, modelled as near-field soil near the underground structure and discretized by the FEM and the far-field effects is included by the scaled boundary finite element method (SBFEM). All of these models are coupled in time domain, and the consistent simulation of the offshore wind turbine can be performed based on the concept idea of partitioned method. The results of simulation show at least a very good performance of partitioned method, also show the reasonable results as we can find at the end of this dissertation.Derzeit gibt es nur wenige unterschiedlich weit fortgeschrittene Projekte, die die Planung und Konstruktion von Offshore-Windkraftanlagen f¨ur die Stromerzeugung behandeln. Die im Offshore-Bereich gegebenen h¨oheren Windgeschwindigeiten k¨onnen geratzt werden, jedoch sind die Anlagen dort anderen Belastungen ausgesetzt, wie bsp. durchwellen. Die Simulation der Material-erm¨udung durch turbulente Winde basiert ¨uberlicherweise auf die Monte Carlo Methode. In der Offshore-Umgebung muss ein gekoppeltes System, bestehent aus der Struktur, dem Fundament, dem Untergrund, dem aerodynamischen Windsystem und dem hydrodynamischen Wellenmodell betrachted werden. In dieser Arbeit werden zun¨achst diese Teilmodelle einzeln entwickelt und werden dann konsistent zum Gesamtsystem gekoppelt. Die Teilsysteme werden beschrieben durch : ˆ das Struktur-Teilsystem, das mit einer nichtlinearen Finit Elemente Methode f¨ur grosse verschiebungen simuliert wird, ˆ das aerodynamische Teilsystem mit vorgechriebener stochastischer Windcharacteristik und unserem instation¨aren dynamischen Stall-Modell fr die aeroelastische Belastung der Fl¨ugel, ˆ das hydrodynamische Teilsystem, das haupts¨achlich als Potentialfluss modelliert wird und mit dem stochastischen Wellenfeld gekoppelt ist, welches auch das Fermfeld ber¨uctsichtigt, um realistische Wellen zu beschreiben. Die Berechnungen dieses Teilsystems basieren auf der Randelemente Methode und nutzt zur schnellen l¨osung die Fast Multipole Methode, ˆ das dynamische Teilsystem f¨ur den Untergrund. Es wird im Nahfeld der Struktur durch die FE-Methode und im Fernfeld durch die SBFE-Methode bechrieben. All diese Modelle werden im Zeitgebiet verbunden, und die konsistente Gesamtsimulation der Offshore-Windkraftanlage kann durchgef¨uhrt werden; gr¨undete auf der Konzeptidee der verteilten Methode. Die Resultate der Simulation zeigen mindestens eine sehr gute Leistung der verteilten Methode, zeigen aber auch die angemessenen Resultate, die am Ende dieser dissertation zu finden sind

Elements of a Computational Framework for Coupled Simulations

International audienceCoupled problems arise because certain aspects of some systems have previously been modelled separately, assuming (implicitly) an uncoupled behaviour. More often then not, computational approaches and mature software have been developed for each of these aspects in isolation. If one has to consider now the coupled problem, it would be advantageous if this previous work could be put to good use. This, in particular, concerns the developed software. In this presentation we will analyse the requirements for this to be achieved, and outline some of the possible solutions. Several tasks have to be accomplished: Non-matching spatial grids and geometric representations have to be joined, fulfilling certain consistency requirements. Similarly non-matching time-stepping schemes have tobe combined. After outlining a possible mathematical formulation for the coupling, the joining of the software will be considered. We view the original software which is modelling some aspect as a software-engineering component, and we describe a component-based approach to achieve a consistently coupled and (if so desired) distributed computational simulation