Offshore wind turbines are designed and analyzed using comprehensive simulation tools (or codes) that account for the coupled dynamics of the wind inflow, aerodynamics, elasticity, and controls of the turbine, along with the incident waves, sea current, hydrodynamics, mooring dynamics, and foundation dynamics of the support structure. This paper describes the latest findings of the code-to-code verification activities of the Offshore Code Comparison Collaboration Continuation project, which operates under the International Energy Agency Wind Task 30. In the latest phase of the project, participants used an assortment of simulation codes to model the coupled dynamic response of a 5-MW wind turbine installed on a floating semisubmersible in 200 m of water. Code predictions were compared from load case simulations selected to test different model features. The comparisons have resulted in a greater understanding of offshore floating wind turbine dynamics and modeling techniques, and better knowledge of the validity of various approximations. The lessons learned from this exercise have improved the participants’ codes, thus improving the standard of offshore wind turbine modeling.

SUMMARYBased on a mixed formulation approach, africtional contact element is proposed for the numerical solution of contact problems including strongly curved rigid obstacles. The implementation of the frictional contact element is analogous to that of a finite element. This feature facilitates its implementation in implicit finite element programmes, since the structure of the code need not be modified.For efficient modelling of the forming tool geometries by Computer Aided Geometric Design techniques and in order to achieve a high performance of the contact search, the numerical schemes of the frictional contact element operate directly on parametric polynomial surface patches. Thus, no discretization of curved contact surfaces is performed.Numerical simulations of deep drawing processes demonstrate the performance of the method in the case of large sliding increments upon curved tools and in the case of elasto-plasticity.KEY WORDS. curved unilateral contact; augmented Lagrangian; frictional contact element INTRODUCTIONDue to the importance of frictional contact in industrial processes, many numerical methods have been developed recently in order to include this additional non-linearity in the numerical simulation. Most of the methods (penalty,' -4 penalty-d~ality,~ fixed point iteration,6 Lagrange multiplier^,^^ mathematical programming,9 complementary pivot methodlo) are efficient for simple applications (flat obstacle, elastic material behaviour, small slip increments). However, severe convergence problems are frequently encountered when implicitly solving frictional contact problems involving severe curvatures and strongly non-linear material behaviour.Within the last few years, one of the most popular approaches was the augmented Lagrangian method, initially introduced by Hestenes' ' and Powell'2 for solving non-linear programming problems with equality constraints. It was extended to treat convex differentiable optimization problems with inequality constraints like the frictionless contact problem by Rockafellar.' Lately, within the context of finite element methods, augmented Lagrangian approaches have been successfully applied to frictionless' 4, ' and frictional contact problems.' 6 -2 0In this paper, an extension of the augmented Lagrangian framework for an implicit treatment of frictional contact, particularly in the case of strongly curved rigid obstacles, will be given. Friction will be described by Coulomb's law. In order to formulate implicitly the laws of

The main concern of the present publication is the computation of dynamic loads of wind turbine power trains, with particular emphasis on planetary gearbox loads. The applied mathematical approach relies on a non‐linear finite element method, which is extended by multi‐body system functionalities, and aerodynamics based on the blade element momentum theory. Copyright © 2007 John Wiley & Sons, Ltd.

A consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed. The approach is based on an augmented Lagrangian approach coupled to an implicit quasi-static Finite Element Method. Analogous to classical work hardening theory in elasto-plasticity, the frictional work is chosen as the internal variable for formulating the evolution of the friction convex. In order to facilitate the implementation of a wide range of phenomenological models, the friction coefficient is defined in a parametrised form in terms of Bernstein polynomials. Numerical simulation of a 3D deep-drawing operation demonstrates the performance of the methods for predicting frictional contact phenomena in the case of large sliding paths including high curvatures.

Defects on wind turbines such as power train misalignments or blade pitch angle deviations are dealt with. These defects cause additional dynamic excitations and thus can reduce the fatigue life of wind turbine components.In order to improve the reliability of dynamic load computations and related fatigue dimensioning of wind turbines, a highly discretized simulation model that incorporates potential system defects is set up. A sensitivity analysis of the impact of system defects on power train dynamics is performed. Experimental measurements of gearbox orbital paths and of the corresponding torque arm loads could be reproduced with good correlation when the simulation model was complemented by power train misalignments and by blade pitch angle deviations. Comparisons of experimental and numerical data are presented in time and frequency domains. Feasible consequences about the impact of alignment defects on the resulting fatigue damage are presented.