Structural optimization with fatigue and ultimate limit constraints of jacket structures for large offshore wind turbines

The purpose of the research presented in this paper is to develop and implement an efficient method for analytical gradient-based sizing optimization of a support structure for offshore wind turbines. In the jacket structure optimization of frame member diameter and thickness, both fatigue limit state, ultimate limit state, and frequency constraints are included. The established framework is demonstrated on the OC4 reference jacket with the NREL 5 MW reference wind turbine installed at a deep water site. The jacket is modeled using 3D Timoshenko beam elements. The aero-servo-elastic loads are determined using the multibody software HAWC2, and the wave loads are determined using the Morison equation. Analytical sensitivities are found using both the direct differentiation method and the adjoint method. An effective formulation of the fatigue gradients makes the amount of adjoint problems that needs to be solved independent of the amount of load cycles included in the analysis. Thus, a large amount of time-history loads can be applied in the fatigue analysis, resulting in a good representation of the accumulated fatigue damage. A reduction of 40 % mass is achieved in 23 iterations using the CPLEX optimizer by IBM ILOG, where both fatigue and ultimate limit state constraints are active at the optimum.