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Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'Whole-life foundation and structure integrity' taking place on Wednesday, 12 March 2014 at 14:15-15:45. The meet-the-authors will take place in the poster area.

Michael Hänler Windrad Engineering GmbH, Germany
Thomas Bauer (1) F P Michael Hänler (1)
(1) Windrad Engineering GmbH, Bad Doberan, Germany

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Cost-optimized design of tubular steel support structures


Steel support structures (towers, monopiles, etc.) are among the most costly components of wind turbines. As a consequence, all efforts have to be made to use cost-optimized solutions for specific wind turbines and environments. Increasing hub heights and installation in deeper water pose high demands on support structures. In our talk we show a systematic approach to design optimized support structures taking into account all the static and dynamic challenges of modern WEC.


For hub heights beyond 120 m the tower frequency becomes a major cost and design driver in onshore application due to the logistic restrictions in tower diameter. Likewise for offshore wind turbines in monopiles the vibration frequency is largely determining the design.
In this talk we describe a systematic approach to design towers and, more general, steel support structures taking into account all necessary static and dynamic requirements. The procedure is based on state of the art algorithms for constrained optimization. With our method it is possible to find the minimum structural mass under a variety of constraints, among them maximum allowed diameter for transportability, available shell dimensions, shell buckling, category of welding seams, vibration frequencies, brittle fracture and vortex induced vibrations. The basic steel quality is chosen by the user. All relevant resistances and detail categories are filled in according to Eurocode 3. Further the soil structure interaction is taken into account for raft foundation as well as for monopiles (p-y-curves).
The algorithm allows predefine the relevant dynamic behaviour (mainly first and second vibration mode) such that that different dynamically equivalent designs will not change the overall WEC loads. This feature enables us to reduce the necessary number of load calculation loops in the design phase of a wind turbine. Depending on the user requirements, it is possible to define the outer geometry and just optimize the shell thickness (works fast, typical for stiff towers) or even to find the optimum diameter within a certain range (soft towers with requirements for second vibration mode).

Main body of abstract

In a nutshell, designing a cost-optimized steel structure is a challenging task, because the structure depends on the loads, and the structure in turn has an impact on the loads. This fact leads to a possible time consuming iteration process.
The structures impact on the loads is mostly driven by the natural frequencies, which makes the optimization even more challenging, because the structures eigenfrequency non-locally depends on the geometry of the structure.
A common steel tower consists of numerous steel shells, with variable diameters and wall thicknesses, which are welded to several sections. On the sections ends, flanges are welded, which are later on assembled and fixed with bolts on the construction site.


1. Shells
With the developed algorithm herein, the optimal wall thicknesses for every shell can be determined with respect to the user given constraints and parameters.
The constraints are:
1. Proof of utilization against buckling (axial, shear and total buckling)
2. Proof of welded seams
3. minimum and or maximum of 1st and/ or 2nd eigenfrequency
The parameters are:
*Initial tower geometry (shell diameters, shell heights)
*Extreme loads in tower top (extreme loads in the remaining shells may be extrapolated) or shell wise
--Simple loads: Shear Forces and Bending Moment, or
--Detailed loads: Isochronal loads for forces and moments in the three main directions
*Loads at MSL for monopiles (especially impact of 50 years wave)
*Fatigue loads (load spectra) in every shell
*Steel type (S355, S275, …)
*FAT-Class of welded seams (100, 90, …)
*Available wall thicknesses
*Tower head mass
*Foundation types
1. Raft foundation -- Simple: Stiffness, or--Detailed: Geometry of foundation
2. Piled foundation -- (Linear) p-y-curves for existing soils at site
First of all, the wall thicknesses are optimized for every shell with respect to the utilization of axial, shear and total buckling, and the utilization of the welded seams. The calculated utilization ratios are based on the equations given in the respective guidelines (Eurocode 3, Part 1-6 and 1-9) and the user given parameters.
This leads to load optimized wall thicknesses for every shell, i.e. the tower is withstands the loads with the lowest possible amount of steel. However, the tower might not fulfil the required minimum 1st and/ or 2nd eigenfrequency; therefore, finally the shells are optimized with respect to the frequency, as described below.
The eigenfrequencies are calculated by beam theory. The soil structure interaction is consideread via the stiffness of the raft foundation or piled foundation. The stiffness of the raft foundation is determined by its geometry and the soil; the stiffness of the piled foundation has to be determined self consistently, because the stiffness depends on the actual deflection (p-y-theory), and the deflection on the actual stiffness.
If the eigenfrequencies of the load optimized tower do not fulfil the frequency constraints, the stiffness of the tower has to be increased, i.e. the wall thicknesses of certain shells. In order to gain a maximum increase in frequency with a minimum amount of steel, the algorithm increases the wall thickness of the shell, where the fraction of frequency gain to additional steel mass is maximal.
For soft towers it is of interest, to reach a certain minimum 2nd eigenfrequency while not trespass a certain 1st eigenfrequency. In such cases the algorithm involves changes of the tower diameter in certain regions.
The constrained optimization algorithm can also be used for the flanges. Again, the object is to design flanges with minimum weight.

The constraints are:
*Proof of utilization (according to Seidel)
*Proof of bolts

The parameters are:

*Extreme bending moments in flanges
*Fatigue loads (Markovian Matrix) in flanges
*Type of bolts (M36, M42, …)
*Type of flange geometry (L-, T-type)
*Type of connection (bolted, thread , anchor joints)

While the optimal tower shells are definite, the optimal flange are only definite based on the number of bolts. Hence, our algorithm determines the optimal flange geometries for the diameter dependent minimum to maximum number of bolts.


Due to the strict constraint optimization approach it is possible to layout support structures for WEC in a cost-optimized way. A big variety of constraints are already implemented in the standard approach. First of all constraints are handled which are connected to loads. These are shell buckling, ultimate stress and weld seam fatigue. Like pure geometrical constraints on diameter and/or shell thickness these are essentially local constraints. Our method combines them in a natural way with global dynamical constraints like natural frequencies. These frequency constraints may be handled as single or double sided constraints upon user requirements. In order to get good approximations of the natural frequencies the soil structure interaction is implemented for different types of foundations. Among them the widely used raft foundation, where the soil spring is calculated according to the model of Hsieh and Lysmer, see [1]. For monopoles we adapted the widely used p-y-curve model. Based on the algorithms described above a computer program for the design of optimized steel tubular structures was developed. The program allows fast determination of the cost-optimized tower shell and flanges (geometry and number of bolts). At the same time it includes typical certification features like defining the necessary steel notch toughness to fulfil the brittle fracture demands or the fatigue damage caused by vortex induced vibrations. Finally our approach enables an optimized layout of support structures reducing the CAPEX costs on one side and accelerates the design process due to the reduction of necessary load calculation loops on the other side.

Learning objectives
-How to use constrained optimization for cost optimized support structure layout
-How to implement single and double sided constraints
-Differences between local and global constraints and how to handle them

[1] –J.A. Studer, J. Laue, M. G. Koller; Bodendynamik , Springer Berlin-Heidelberg, 2007