Offshore wind turbines are relatively complex structural and mechanical systems located ina highly demanding environment. In this study, the fundamental aspects and major issues related to the design of such structures are inquired. The system approach is proposed to carry out the design of the structural parts: in accordance with this philosophy, a decomposition of the system (environment, structure, actions/loads) and of the structural performance is carried out, in order to organize the qualitative and quantitative assessment in various sub-problems. These can be faced by sub-models of different complexity both for the structural behavior and for the load models. Numerical models are developed to assess the safety performance under aerodynamic and hydrodynamic actions. In the structural analyses, three types of turbine support structures have been considered and compared: a monopile, a tripod and a jacket.

1. Structural Design and Analysis of Offshore Wind
Turbines from a System Point of View
by
Francesco Petrini, Sauro Manenti, Konstantinos Gkoumas, Franco Bontempi
R EPRINTED
FROM
WIND ENGINEERING
VOLUME 34, N O . 1, 2010
M ULTI -S CIENCE P UBLISHING C OMPANY
5 WATES WAY • B RENTWOOD • E SSEX CM15 9TB • UK
T EL : +44(0)1277 224632 • FAX : +44(0)1277 223453
E-MAIL: mscience@globalnet.co.uk • WEB SITE: www.multi-science.co.uk

2. W IND E NGINEERING VOLUME 34, N O . 1, 2010
PP
85–108
85
Structural Design and Analysis of Offshore Wind
Turbines from a System Point of View
Francesco Petrini1, Sauro Manenti2, Konstantinos Gkoumas3, Franco Bontempi*,4
1Department
of Structural and Geotechnical Engineering, University of Rome “La Sapienza”, via
Eudossiana, 18 - 00184 Rome, Italy (francesco.petrini@uniroma1.it)
2Department of Hydraulics Transportation and Roads, University of Rome “La Sapienza”, via
Eudossiana, 18 - 00184 Rome, Italy (sauro.manenti@uniroma1.it)
3Department of Hydraulics Transportation and Roads, University of Rome “La Sapienza”, via
Eudossiana, 18 - 00184 Rome, Italy (konstantinos.gkoumas@uniroma1.it)
4Department of Structural and Geotechnical Engineering, University of Rome “La Sapienza”, via
Eudossiana, 18 - 00184 Rome, Italy (franco.bontempi@uniroma1.it)
ABSTRACT
Offshore wind turbines are relatively complex structural and mechanical systems located in
a highly demanding environment. In this study, the fundamental aspects and major issues
related to the design of such structures are inquired. The system approach is proposed to
carry out the design of the structural parts: in accordance with this philosophy, a
decomposition of the system (environment, structure, actions/loads) and of the structural
performance is carried out, in order to organize the qualitative and quantitative assessment
in various sub-problems. These can be faced by sub-models of different complexity both for
the structural behavior and for the load models. Numerical models are developed to assess
the safety performance under aerodynamic and hydrodynamic actions. In the structural
analyses, three types of turbine support structures have been considered and compared: a
monopile, a tripod and a jacket.
1. INTRODUCTION
Offshore wind turbines (OWT) emerge as an evolution of the onshore plants for which the
construction is a relatively widespread and consolidated practice providing a renewable
power resource [1]. In order to make the wind generated power more competitive with
respect to conventional exhaustible and high environmental impact sources of energy, the
attention has turned toward offshore wind power production [2].
Besides being characterized by a reduced visual impact, since they are placed far away
from the coast, OWTs can take advantage from more constant and intense wind forcing,
something that can increase the amount and regularity of the productive capacity and make
such a resource more cost-effective if the plant is lifelong and operates with minimum
interruption through its lifespan.
From a general point of view, an OWT is formed by both mechanical and structural
elements. Therefore, it is not a “common” civil engineering structure; it behaves differently
according to different circumstances related to the specific functional activity (idle, power
*Corresponding
author

3. S TRUCTURAL D ESIGN
86
AND
A NALYSIS
OF
O FFSHORE W IND T URBINES
S YSTEM P OINT OF V IEW
FROM A
Blades – Rotor – Nacelle
Tower
Transition
platform
MONOPILE
TRIPOD
JACKET
Water level
Substructure
Support
structure
Sea floor
Foundation
Seabed
Foundation
Figure 1: Main parts of an offshore wind turbine for different support structures.
production, etc), and it is subject to highly variable loads (wind, wave, sea currents loads, etc.).
In the design process, different structural schemes for the supporting structure can be
adopted (Figure 1), mainly depending on the water depth, which determines the
hydrodynamic loads acting on the structure and drives the choice of the proper techniques for
the installation and maintenance of the support structure.
Moreover, since the structural behavior of OWTs is influenced from nonlinearities,
uncertainties and interactions, they can be defined as complex structural systems [3].
The above considerations highlight that a modern approach to study such structures has
to evolve from the idea of “structure” itself, intended as a simple device for channeling loads,
to the one of “structural system”, intended as “a set of interrelated components which interact
one with another in an organized fashion toward a common purpose” [4]. This system
approach includes a set of activities which lead and control the overall design,
implementation and integration of the complex set of interacting components [5,6].
In this study, the original definition by NASA [4] has been extended in such a way that the
“structural system” organization contains also the actions and loads. The latter derive from,
and are strictly related to, the environment (Figure 2).
A certain amount of complexity arises from the lack of knowledge and from the modeling
of the environment in which the turbine is located. In this context two main design issues can
be individuated: the consideration of the uncertainty deriving from the stochastic nature of
the environmental forcings (in particular aerodynamic and hydrodynamic) and the proper

4. W IND E NGINEERING VOLUME 34, N O . 1, 2010
87
PERFORMANCE
Structural system
ENVIRONMENT
Interaction
STRUCTURE
ACTIONS
Figure 2: Structural system organization.
Wind and wave flow
ENVIRONMENT ZONE
EXCHANGE ZONE
Aerodynamic and
aeroelastic
phenomena
Wind site basic
parameters
Structure
Wave site basic
parameters
Site-specific
environment
Structural (nonenvironmental)
system
Wind, wave and
sea current
actions
Nonenvironmental
solicitations
Other
environmental
agents
Hydrodynamic
phenomena
Types of uncertainties
Propagation
1.
2.
3.
Aleatoric
Epistemic
Model
Propagation
1.
2.
3.
Aleatoric
Epistemic
Model
1.
2.
3.
Aleatoric
Epistemic
Model
Figure 3: Generic depiction of the uncertainties and the interaction mechanisms in the design of an
offshore wind turbine structure.
modeling of the possible presence of non linear interaction phenomena between the different
actions and between the actions and the structure.
In general, uncertainties can spread during the various analysis phases that are developed
in a cascade. The incorrect modeling of the involved uncertainty can lead to an incorrect
characterization of the structural response from a stochastic point of view and, thus, to an
improper quantification of the risk for a given structure subjected to a specific hazard.
Having as a goal the schematization of the problem and the individuation of the
uncertainty propagation mechanisms, reference can be made to the Figure 3, where the
process of the environmental actions generation is qualitatively represented also with
considerations on the involved uncertainties.
Following the wind and the hydrodynamic flows impacting on the structure, it is possible
to distinguish two zones:
•
Environment zone: it is the physical region sufficiently close to the structure to
assume the same environmental site parameters of the structure, yet far enough to
neglect the flow field perturbations (in terms of particle’s trajectories, pressure field,
etc.) induced by the presence of the structure itself. In the environment zone, the
wind and the hydrodynamic flows can interact with each other and with other
environmental agents, changing their basic parameters. The physical phenomena
and uncertainties in the environment zone propagate in the neighborhood regions.

5. S TRUCTURAL D ESIGN
88
AND
A NALYSIS
OF
O FFSHORE W IND T URBINES
S YSTEM P OINT OF V IEW
FROM A
•
Exchange zone: it is the physical region adjoining the structure. In this zone, the
structure itself, the wind and the hydrodynamic field experience the mechanical
interchange (aerodynamic and hydrodynamic phenomena) from which the
actions arise. In the exchange zone, some non-environmental solicitations are
present; these solicitations may change the dynamic or aerodynamic
characteristics of the original structure; so the actions are generated considering
this structural sub-system (original structure combined with non-environmental
solicitations) instead of regarding only the original structure itself. By definition,
physical phenomena and uncertainties cannot propagate from the exchange zone
to the environment zone.
In general, the uncertainties can be subdivided in three basic typologies:
•
aleatory uncertainties (arising from the unpredictable nature of the magnitude, the
direction and the variance of the environmental actions);
•
epistemic uncertainties (deriving from the insufficient information and the errors in
measuring the previously mentioned parameters);
•
model uncertainties (deriving from the approximations in the models).
Regarding for example the wind model and considering the turbulent wind velocity field
as a Gaussian stochastic process, an uncertainty related to the hypothesis of Gaussianity is
introduced.
The aleatory uncertainties can be treated by carrying out a semi-probabilistic (looking for
the extreme response) or a probabilistic analysis (looking for the response probabilistic
distribution) analysis.
A possible way to reduce the model uncertainties is given by differentiating the modeling
levels. This can be carried out not only for the structural models, but also for the action and
interaction phenomena models; for this reason different model levels are adopted (for the
sake of simplicity, the epistemic uncertainties are not considered in this study).
A suitable tool to govern the complexity is given from the structural system
decomposition, represented by the design activities related with the classification and the
identification of the structural system components, and by the hierarchies (and the
interactions) between these components.
As mentioned before, the decomposition regards not only the structure, but also the
environment and the actions and loads, and it is the subject of the first part of this study.
Furthermore, due to the complexity, the design of these structures has to be carried out
under a Performance-Based Design philosophy: different aspects and performance under
different loading conditions (with reference to all possible system configurations that can be
assumed by the blades and the rotor) have to be investigated for this type of structures.
Additional design issues related to the structural aspects are mentioned below with some
proper references:
•
Aerodynamic optimization [7].
•
Foundation design and soil-structure interaction [8, 9, 10].
•
Fatigue calculations [11, 12].
•
Vessel impact and robustness [13].
•
Life Cycle assessment [14, 15].
•
Marine scour [16, 17].
•
Possible floating supports [18, 19].
•
Standards certification [20, 21, 22, 23, 24, 25].

6. W IND E NGINEERING VOLUME 34, N O . 1, 2010
89
Figure 4: Different views of the jacket support structure adopted after the numerical analyses.
Finally, an important issue for offshore wind turbines is the choice of the support structure,
related principally to the water depth, the soil characteristics and economic issues. If the
water depth (h) is considered as the principal parameter, according to the DNV-OS-J101 [22],
the following rough classification can be made: monopile, gravity and suction buckets
(h < 25m); tripod, jacket and lattice tower (20m < h < 40–50m); low-roll floaters and tension leg
platform (h > 50m). In this study focus is given to monopile, tripod and jacket support
structures.
The paper starts with the description of the system approach applied to OWT design: while
the system point of view is a consolidated practice in many engineering fields (e.g. aerospace
engineering), in the case of OWTs, it is not fully established and represents an ongoing process.
In the second part of the paper, the system point of view is applied to the numerical modeling
of a case study. More precisely, numerical analyses are carried out on different OWT support
structures. The obtained results justify the adoption of a jacket structure for the specific case
(Figure 4).
2. STRUCTURAL SYSTEM DECOMPOSITION
As previously stated the decomposition of the structural system is a fundamental tool for
the design of complex structural systems, and it has to be performed together with the
decomposition of the performance the structure has to fulfill (Figure 5). The
decomposition is carried out focusing the attention on different levels of detail: starting
from a macro-level vision and moving on towards the micro-level details (for more details
see Bontempi et al. [26]).
2.1. Decomposition of the Environment
The first step of the structural system decomposition concerns the environment. This is due
to the fact that, in a global approach, the structure is considered as a real physical object
placed on an environment where a variety of conditions, strictly related to the acting loads,
should be taken into consideration. Their decomposition is performed in the first column of
Figure 5.

7. S TRUCTURAL D ESIGN
90
AND
A NALYSIS
OF
O FFSHORE W IND T URBINES
S YSTEM P OINT OF V IEW
FROM A
ENVIRONMENT
STRUCTURE
ACTIONS/LOADS
Main structure
Gravitational / Inertial
Wind conditions
Normal wind conditions
Rotor–nacelle assembly
Extreme wind conditions
Marine conditions
Junctions/bearings
Waves
Junctions/bearings
Extreme wave conditions
Junctions/bearings
Water level
Actuation
Tower
Seabed movement and scour
Torque control
Junctions
Other conditions
Yaw and pitch actuator loads
Substructure
Mechanical breaking loads
Junctions
Air temperature
Other
Foundations
Humidity
Wake loads
Junctions
Solar radiation
Impact loads
Secondary structure
Rain, hail, snow, ice
Wave
Current
Support structure
Marine growth
Aerodynamic
Hydrodynamic
Blades
Sea currents
Aviation
Seismic activity
Rotor
Normal wave conditions
Gravity
Braking
Nacelle
Chemically active substances
Mechanically active substances
Tsunami
Energy production
Energy transfer
Auxiliary structure
Environmental aggressiveness
Seismicity
Operation
Water density
Maintenance
Water temperature
Emergency
Lighting
Maritime traffic
PERFORMANCE
Serviceability
Safety
Service Limit States –SLS
Reliability
Ultimate Limit States –ULS_1
Deflections/Displacements
Stress limit
Vibrations
Strain limit
Buckling
Ultimate Limit States –ULS_2
Degradation effects
Fatigue Limit States –FLS
Robustness
Accidental Limit States –ALS
Impact
Explosion
Fire
Figure 5: Structural system and performance decomposition of an offshore wind turbine.
2.2. Decomposition of the Structure
The second step of the decomposition relates to the offshore wind turbine structure. This is
organized hierarchically, considering all the structural parts categorized in three levels
(second column of Figure 5):
•
Macroscopic (macro-level), related to geometric dimensions comparable with
the whole construction or parts with a principal role in the structural behavior;
the parts so considered are called macro components which can be divided
into:
–
–
the main structure, that has the objective to carry the main loads;
the secondary structure, connected with the structural part directly loaded
by the energy production system;
–
the auxiliary structure, related to specific operations that the turbine may
normally or exceptionally face during its design life: serviceability,
maintainability and emergency.

8. W IND E NGINEERING VOLUME 34, N O . 1, 2010
91
Focusing the attention on the main structure, it consists in all the elements that form the
offshore wind turbine. In general, the following segments can be identified:
a.
b.
•
support structure (the main subject of this study);
rotor-nacelle assembly.
Mesoscopic (meso-level), related to geometric dimensions still relevant if compared
to the whole construction but connected with specialized role in the macro
components; the parts so considered are called meso-components. In particular the
support structure can be decomposed in the following parts:
a.
foundation: the part which transfers the loads acting on the structure into the
seabed;
b.
substructure: the part which extends upwards from the seabed and connects
the foundation to the tower;
c.
•
tower: the part which connects the substructure to the rotor-nacelle assembly.
Microscopic (micro-level), related to smaller geometric dimensions and specialized
structural role: these are simply components or elements.
2.3. Decomposition of the Actions and Loads
The next step of the structural system decomposition is the one regarding the actions related
to the environmental conditions. These are decomposed as shown in the third column of
Figure 5, from which the amount of the acting loads can be comprehended.
It is important to underline that, since the environmental conditions in general are of
stochastic nature, the magnitude of the actions involved is usually characterized, from a
statistical point of view, by a return period TR: lower values of TR are associated with the so
called “normal conditions”, while higher values of TR are associated with “extreme conditions”.
2.4. Performance Decomposition
As a final step, the performance requirements are identified and decomposed as follows
(lower part of Figure 5).
•
Assurance of the serviceability (operability) of the turbine, as well as of the
structure in general. As a consequence, the structural characteristics (stiffness,
inertia, etc.) have to be equally distributed and balanced along the structure;
•
Safety assurance with respect to collapse, in plausible extreme conditions; this is
applicable also to the transient phases in which the structure or parts of it may
reside (e.g. transportation and assembly), and that have to be verified as well;
•
Assurance of an elevated level of reliability for the entire life-span of the turbine. As
a consequence, a check of the degradation due to fatigue and corrosion phenomena
is required;
•
Assurance of sufficient robustness for the structural system, that is to ensure the
proportionality between an eventual damage and the resistance capacity,
independently from the triggering cause, ensuring at the same time the survival of
the structure under a hypothetical extreme condition.
The following performance criteria can be identified for the structural system, leading
eventually to the selection of appropriate Limit States:
•
Dynamic characterization of the turbine as defined by the functionality
requirements, regarding the:
–
natural vibration frequencies of the whole turbine, including the rotor-nacelle
assembly, the support structure and the foundations;

9. S TRUCTURAL D ESIGN
92
AND
A NALYSIS
OF
O FFSHORE W IND T URBINES
S YSTEM P OINT OF V IEW
FROM A
–
compatibility of the intrinsic vibration characteristics of the structural system
with those of the applied forces and loads;
–
compatibility of the displacement and the acceleration of the support system
with the functionality requirements of the turbine.
•
Structural behavior with respect to serviceability (SLS- Serviceability Limit State),
regarding the:
–
–
•
limitation of deformations;
prevention of any loosening of the connections.
Preservation in time of the structural integrity, regarding the:
–
–
•
durability for corrosion;
structural behavior with respect to fatigue (FLS-Fatigue Limit State).
Structural behavior under near collapse conditions (ULS-Ultimate Limit State),
regarding the:
–
assessment of the stress state for the whole structure, its parts, elements and
connections;
–
–
•
assessment of the global resistance of the structural system;
assessment of the resistance for global and local instability phenomena.
Structural behavior in presence of accidental scenarios (ALS-Accidental Limit
State), regarding the:
–
provisions for the decrease in the load bearing capacity proportional to the
damage (the concept of structural robustness- see for example Starossek [27]
and Bontempi et al. [28]);
–
provisions for the survival of the structural system in presence of extreme
and/or unforeseen, situations; these include the possibility of a ship impacting
the structural system (support system or blades), with consequences
accounted for specific risk scenarios.
3. ENVIRONMENT AND ACTION MODEL
From all the loads indicated in Paragraph 2.3, in this study attention is focused on the
aerodynamic and the hydrodynamic ones.
Typically, an environmental action, when observed during a short time period, is made of
two components: a mean (or slowly variable) component, and a stochastic one. For the
aerodynamic and the hydrodynamic actions, the mean component is generated respectively
by the mean wind velocity and by the sea current, while the stochastic component is
generated respectively from the turbulence wind velocity and from the linear waves.
The definition of “mean” has to be specified with reference to a specified “short time
period” (usually less than 1 hour); in contrast, the so called “mean component” varies in a
stochastic manner during long time periods. For this reason, in what follows the mean
components will be considered as constant only for short periods of analyses.
The generic environmental configuration is shown in Figure 6, where the macrogeometric parameters defining the problem are also represented. These are the local mean
water depth (h), the hub height above the mean water level (H) and the blade length (or rotor
radius, R).
Correct prediction of the structural response under extreme and normal load
conditions requires the definition of their probability distribution and statistical

10. W IND E NGINEERING VOLUME 34, N O . 1, 2010
93
WP (t)
P
uP (t)
VP (t)
Turbulent
wind
W
ate
r le
ve
l (m
P
Vm (zP)
Mean
wind
ea
n)
R
Hub
Waves
Mu
level
z
dl
ine
H
y
Vw (z′) y′
x, x′
Current
z′
Vcur (z′)
vel
ter le
n)
(mea
Wa
h
e
d lin
Mu
Figure 6: Problem statement and configuration of the actions.
parameters; these are site specific, and have to be estimated by carrying out statistical
analyses of the measurements database. In particular two kinds of investigations are
usually carried out: short term statistics for fatigue analysis, and long term statistics, for
ultimate limit state analysis.
Finally, the definition of the extreme load cases requires an estimation of the probability
distribution for: (i) the extreme 10-min average wind velocity at the reference height, and (ii)
the significant wave height estimated in a 3-hour reference period along with the associated
spectral peak period.
When no information is available for defining the long term joint probability distribution of
extreme wind and waves, it shall be assumed that the extreme 10-min mean wind speed with
a 50-year recurrence period occurs during the extreme sea state with a 50-year recurrence
period (IEC 64100-3 [25]) adopting appropriate reduced values.
3.1. Aeolian and Hydrodynamic Fields Model
Concerning the wind modeling for the computation of the aerodynamic action, a Cartesian
three-dimensional coordinate system (x,y,z), with origin at the mean water level and the zaxis oriented upward is adopted. Focusing on a short time period analysis, the three
components of the wind velocity field Vx ( j ), Vy ( j ), Vz ( j ) at each spatial point j (the variation
with time is omitted for the sake of simplicity) can be expressed as the sum of a mean (timeinvariant) value and a turbulent component u(j ), v(j), w(j) with mean value equal to zero.

11. S TRUCTURAL D ESIGN
94
AND
A NALYSIS
OF
O FFSHORE W IND T URBINES
S YSTEM P OINT OF V IEW
FROM A
Assuming that the mean value of the velocity is non-zero only in x direction, the three
components are given by:
Vx (j) = Vm(j) + u(j ); Vy ( j ) = v(j ); Vz ( j ) = w(j)
(1)
The mean velocity Vm(j) can be determined by a database of values recorded at or near the
site, and evaluated as the record average over a proper time interval (e.g. 10 minutes), while
the variation of the mean velocity Vm with the height z over a horizontal surface of
homogeneous roughness can be described by an exponential law. Finally, the turbulent
components of the wind velocity are modeled as zero-mean Gaussian ergodic independent
processes. By using the proposed model, it is possible to generate samples of the wind action
exerted at each point j of the structure.
Concerning the hydrodynamic actions, as previously stated, they are due to currents and
waves. For what concerns the sea currents induced by the tidal wave propagation in shallow
water condition (i.e. the ratio between water depth h and wave length L is lower than 0.05), in
general they are characterized by a sub-horizontal velocity field, while their intensity
decreases slowly with the depth. Waves act on the submerged structural elements and on the
transition zone above the water-air interface; in the first case actions are the result of the
alternative motion of fluid particles, induced by the fluctuating perturbation of the liquid
surface; in the second case the action is the consequence of the breaking waves, which may
occur in shallow water condition. In general the short period water surface fluctuation, with
respect to the mean sea level, is a time-dependent stochastic variable, and can be described by
means of statistical parameters:
•
the significant wave height HS ; it is defined as four times the mean square root of the
sea elevation process. It represents a statistical measure of the intensity of the wave
climate as well as of the variability in the arbitrary wave heights.
•
the spectral peak period TP ; it is related to the mean zero-crossing period of the sea
elevation process.
For extreme events analysis, in general the significant wave height is defined with respect
to a proper return period TR (DNV-OS-J101 [22]).
For fatigue analysis the sea state is characterized through the wave energy spectral
density, defined upon the domain of frequency and geographic direction of the wave
components: usually this is obtained by multiplying the calculated one-dimensional spectrum
S(f) by a function of directional spreading, symmetric with respect to the principal direction
of the wave propagation [29].
3.2. Aerodynamic and Hydrodynamic Actions Model
In general, the components of the actions could be calculated separately for all structural
elements adopting a common frame of reference and then superimposed by a vector sum in a
phase-correct manner.
The aerodynamic force can be decomposed, as usual, in a drag (parallel to the mean wind
velocity) and a lift (orthogonal to the mean wind velocity) component, while moments have
been neglected in the present paper. These can be computed for each structural component
from the specific wind velocity field and for each structural configurations (for example,
extreme wind and parked turbine configurations), by using well known expressions, as shown
in Bontempi et al. [30] and Petrini et al. [31]. The equivalent static load can be derived through
peak factors, based on the probabilistic characteristics of the wind velocity modeled as a
stochastic process [32].

12. W IND E NGINEERING VOLUME 34, N O . 1, 2010
95
Concerning the hydrodynamic loads on a structural slender cylindrical member (D/L < 0.2,
with: D member diameter normal to the fluid flow, L wave length), both wave and (stationary)
current generate the following two components:
•
A force per unit length acting in the direction perpendicular to the axis of the
member and parallel to the orthogonal (with respect to the member) components
of the water particle velocity (wave vw plus current Vcur induced) and acceleration
(wave only); it can be estimated by means of Morison equation:
 ρ πD 2 ·

1
dF ( z ',t ) = ci wat
vw ( z ',t ) + cd ρwat D vw ( z ',t ) +Vcur ( z ',t )⋅ vw ( z ',t ) +Vcur ( z ',t ) dz '




4
2


(2)
where ρwat is the water density, ci and cd are the inertia (including added mass for a
moving member) and drag coefficient respectively, which are related to structural
geometry, flow pattern and surface roughness: superposed dot indicates the time
derivate, in the Eq. (2). Periodic functions are adopted for both the wave velocities
and accelerations [33].
•
A non-stationary (lift) force per unit length acts in the direction perpendicular both
to the axis of the slender member and to the water current. This component is
induced by vortex shedding past the cylinder and inverts its direction at the
frequency fl of eddies separation which is related to flow field and structural
geometry through Strouhal number St = Dfl /Vcur ; fl should be kept far from the
structure’s natural frequency to avoid resonances.
In the case of static analysis, equivalent static forces are applied considering the amplitude of
the fluctuating actions and, eventually, applying proper load amplification factors.
4. NUMERICAL MODELING OF THE STRUCTURE
As stated in Section 1, a differentiation of the modeling level is adopted to reduce the
uncertainties. The level of a generic model of the structure is here identified by means of two
parameters: the maximum degree of detail and the scale of the model; if the finite element
method is adopted, at each model level it is possible to associate a certain typology of finite
element, which is mainly used to build the model.
In general, four model levels are defined for the structure:
1.
System level (S): the model scale comprises the whole wind farm and can be
adopted for evaluating the robustness of the overall plant; highly idealized model
components are used in block diagram simulators.
2.
Macro level or Global modeling (G): in these models, the scale reduces to the single
turbine structure, neglecting the connections between different structural parts.
The component shapes are modeled in an approximate way, the geometric ratios
between the components are correctly reproduced; beam finite elements are
mainly adopted;
3.
Meso-level or Extended modeling (E): these models are characterized by the
same scale of the previous level but with a higher degree of detail: the actual
shape of the structural components is accounted for and the influence of
geometrical parameters on the local structural behavior is evaluated. Shell
elements are adopted for investigating the internal state of stress and strain (e.g.
for fatigue life and buckling analysis) inside the structure extrapolated from
previous models;

13. S TRUCTURAL D ESIGN
96
AND
A NALYSIS
OF
O FFSHORE W IND T URBINES
S YSTEM P OINT OF V IEW
FROM A
4.
Micro level or Detail modeling (D): this kind of models are characterized by the
highest degree of detail and used for simulating the structural behavior of specific
individual components, including connecting parts, for which a complex internal
state of stress has been previously pointed out e.g. due to the presence of
concentrated loads. Shell or even solid finite elements are used.
The features for different structural model levels are resumed in Table 1; a similar
distinction can be made regarding the specification of the external loads.
According to what said above, at the initial stage of investigation structural analyses have
been carried out with macro-level and meso-level models of the three offshore wind turbine
structure types previously described.
With reference to Figure 7 some of the developed macro-level structural models are shown
for the monopile (left part), tripod (middle) and jacket (right part) support structure.
Model Level
System level
Macro-level
Meso-level
Micro level
Table 1: Definition of the model levels
Maximum Detail Level
Main Adopted
Finite Elements
wind farm
approximate shape of the
BLOCK elements
structural components
single turbine
approximate shape of the
BEAM elements
structural components,
correct geometry
single turbine
detailed shape of the
SHELL, SOLID elements
structural components
individual
detailed shape of the
SHELL, SOLID elements
components
connecting parts
Scale
(a)
(b)
(c)
Emergent
Transition
Z
X
Y
Immersed
Foundation
Figure 7: Macro-level finite element models: monopile (a), tripod (b) and jacket (c).

14. W IND E NGINEERING VOLUME 34, N O . 1, 2010
97
The effect of foundation medium should be simulated with a full non-linear model in order
to account for possible plastic effects and load time-history induced variation of the
mechanical properties. At this level of investigation, an idealized soil has been simulated by
means of both:
•
Linear springs: such technique has been adopted for the macro-level models.
Springs are applied at the pile surface and acts in the two coordinate horizontal
directions: the corresponding mechanical parameters have been set up on the basis
of available soil characteristic and simulates its lateral resistance at the pile
interface;
•
Solid elements: used for meso-level models. These three-dimensional elements
simulate the linear mechanical behavior of the soil. The extension of the foundation
medium included in the model has been selected in order to minimize boundary
effects.
Both kinds of models have been used for evaluating the modal response of the structural
system.
The decomposition of both the structural system and the performance, and the
differentiation of the model levels can be used to guide and optimize the numerical analysis
efforts in this design phase. In this sense, focusing on a certain structural component and
selecting the specific performance, the choice of both model level and type of analysis to
adopt can be done, in such a way, to give the best efficiency of the analysis (deriving from a
suitable balance between the required detail level of outputs and the computational efforts
needed).
For example, focusing the attention on the tower with a steel tubular section, the
maximum stresses for Ultimate Limit State analysis can be preliminary obtained by adopting
a macro-level model and by carrying out a static extreme analysis (characterized by extreme
values of the environmental loads). However, if the local buckling phenomena need to be
assessed, a more detailed meso-level structural model and a static incremental analysis is
required. These considerations are summarized in Table 2.
Structural Component
Table 2: Model and analysis type selection
Performance
Model Level Analysis Type
Macro
Stress safety (ULS)
Static extreme
Meso
Macro
Global Buckling (ULS)
Static incremental
Meso
Tower
Meso
Local Buckling (ULS)
Static incremental
Micro
Macro (poor)
Fatigue (FLS)
Meso
Micro
Dynamic

15. S TRUCTURAL D ESIGN
98
AND
A NALYSIS
OF
O FFSHORE W IND T URBINES
S YSTEM P OINT OF V IEW
FROM A
5. NUMERICAL ANALYSES
The numerical analyses have been conducted for three different support structures:
monopile, tripod and jacket. The principal geometrical and structural features adopted for the
analyses are as follows:
•
hub height positioned 100 m above the mean sea level (m.s.l.);
•
tower with a steel tubular section, with a diameter of 5 m and a thickness of 0.05 m;
•
water depth of 35 m;
•
foundations depth of 40 m;
•
foundation diameter of 6 m (monopile), 2.5 m (tripod and jacket).
For the tripod substructure, the tubular tripod arm diameter and thickness is respectively
of 2.5 m and 0.05 m. For the jacket substructure, the diameter (thickness) of the vertical,
horizontal and diagonal tubular members, is respectively of 1.3 m (0.026 m), 0.6 m (0.016 m)
and 0.5 m (0.016 m). Finally, the tower supports a Vestas-V90 turbine [34] with a rotor diameter
of 90 m.
5.1. Modal Analysis
The preliminary task of the dynamic analysis is to assess the natural modes of vibration in
order to avoid that non-stationary load (e.g. wind and wave induced) could cause the system
resonance when excitation and natural frequencies are closer.
Geometrical parameters of the three support structures have thus been selected with the
aim of maintaining the corresponding natural frequency far from that of the non-stationary
external forcing (wind and wave).
The finite element modal analysis provided the deformed shapes given in Figure 8, where
only odd modes are displayed since modes i and i +1 (with i = 1, 3) have the same frequency but
vibration occurs in orthogonal planes, according to the axial symmetry of the tower (the
eccentric mass of the blades is neglected).
In Figure 9, the two x-parallel dashed lines correspond, respectively, to the mean rotor
frequency (1P) and the frequency of a single blade passing (3P), which is triple with respect to
the former one for a three bladed turbine.
These frequencies determine the sampling period of the wind turbulent eddies and, as a
consequence, the characteristics of the induced non-stationary actions. Therefore, they
(a)
1st
(b)
M0
3rd
M0
1st
(c)
M0
3rd
M0
1st
M0
3rd
M0
Z
X
Y
Z
X
Y
Figure 8: Modal analysis (macro-level models). Natural mode shapes for the monopile (a), tripod (b)
and jacket (c) support structures.

16. W IND E NGINEERING VOLUME 34, N O . 1, 2010
99
2.0
Freq. [Hz]
2.5
Monopile
Tripod
Jacket
1.5
1.0
3P
0.5
1P
0.0
1
3
Mode number
5
Figure 9: Comparison of the natural frequencies.
assume importance when performing dynamic analysis and are generally compared with
respect to the first natural frequency fnat in order to classify the structural behavior:
•
if fnat falls below 1P the structure is called “soft-soft”; for this type of structure the
wave load could be dominant with respect to the wind load, and the fatigue effects
can be significant;
•
if fnat is between 1P and 3P the structure is called “soft-stiff”; for this type of structure
the wind action frequency could be considerable higher than the one due to waves,
and the fatigue effects can be still significant;
•
if fnat is greater than 3P the structure is called “stiff-stiff”; for this type of structure the
fatigue effects in general are not significant.
From the results plotted in Figure 9 it can be seen that the structural system falls in the softstiff range only if the jacket support type is adopted. In the same figure, it can be noted that for
the first couple of modes the dynamic behavior of the jacket is stiffer than the one of the other
types, but the trend inverts from the third mode on.
5.2. Static Analysis Under Extreme Loads
Steady loads have been assumed for the principal environmental actions and no functional
loads are present (parked condition). The external forcing has been characterized by
assuming prudentially a return period larger than the one prescribed by Codes and Standards.
The numerical analysis for the selected support structure types has been carried out
considering the three load cases summarized in Table 3, where:
•
Vhub represents the wind velocity at the hub height;
•
VeN (with N = 1 or 100) represents the maximum wind velocity with a return period
TR equal to N years, derived from the reference wind velocity associated with the
same return period VrefN multiplied by a certain peak factor;
•
VredN represents the reduced wind velocity with a return period TR equal to N years
and it is derived from the previous one by applying a reduction factor;

17. 100
S TRUCTURAL D ESIGN
AND
A NALYSIS
OF
O FFSHORE W IND T URBINES
S YSTEM P OINT OF V IEW
FROM A
Table 3: Load cases
Design
Situation
Load Factors γF
Gravitational Inertial
Combination
Name
Wind
Condition
Marine
Condition
Environmental
6.1b
Vhub=Ve100
H=Hred100
1.35
1.1
1.25
Vhub=Vred100 H=Hmax100
Vhub=Ve1
H=Hred100
1.35
1.35
1.1
1.1
1.25
1.25
Parked
(standstill
or idling)
6.1c
6.3b
In the same table HmaxN and HredN represent respectively the design maximum wave
height and the design reduced wave height associated whit a return period TR equal to N
years.
Steady wind field has been assumed along with stationary and regular wave actions; both
actions have been assumed to act in the same direction.
The design wind exerts a force distribution that is dependent on the undisturbed flow
pattern: the resultant action on the rotor blades has been concentrated at the hub height while
the drag forces acting on the support are distributed along the tower and the exposed piece of
the substructure (jacket type only). The immersed part of the support structure is subject to
combined drag and inertia forces induced by the undisturbed wave and the current induced
flow field.
In Figure 10, the calculated vertical profiles of the aerodynamic and hydrodynamic actions
induced per unit length on the tower and the substructure respectively are shown for the
monopile case. The analyses carried out through macro-level models allowed for evaluation
of both the reactions at the mud line (shear and overturning moment) and the induced
displacement at the hub height.
Results obtained with macro-level models are summarized in Figure 11. The maximum
shear stress at the mud line is reached for the load case 6.1c, i.e. the one characterized by
maximum wave height and reduced wind speed (see Table 3); on the other hand, the
combination giving the maximum bending moment at the mud line corresponds to extreme
wind and reduced wave height (combination 6.1b).
From what above follows that wave and current exert much more influence on the
resultant shear force, while the wind appears to be more critical for the overturning moment,
being distributed at a higher distance from the base.
Aerodynamic
Hydrodynamic
Hydrodynamic
40
120
35
Height
above
sea
level [m]
100
40
35
30
30
Height
above
mud line [m]
80
25
20
15
10
10
5
40
20
15
60
Height
above
mud line [m]
25
5
20
Action [N/m]
0
0
0
5000
Comb 6.1b
Action [N/m]
Action [N/m]
0
10000
Comb 6.1c
0
100000
Comb 6.1b
200000
Comb 6.1c
0
100000
Comb 6.1b
Figure 10: Environmental actions (monopile type support).
200000
Comb 6.1c

18. W IND E NGINEERING VOLUME 34, N O . 1, 2010
101
400000
7000
350000
6000
300000
5000
250000
4000
200000
3000
150000
100000
2000
50000
1000
0
[KN*m]
Monopile
Tripod
6.1b
6.1c
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
[m]
0
[KN]
Jacket
Monopile
6.1b
6.3b
Monopile
Tripod
6.1b
6.1c
Tripod
6.1c
Jacket
6.3b
Jacket
6.3b
Figure 11: Overturning moment, total shear reaction at the mud line and hub displacements, for three
different load cases.
Moreover, from the same figure it can be seen that the three structural types experience
approximately the same resultant shear and moment under each load combination.
Concerning the horizontal displacement at hub height, it can be seen an increasing stiffness of
the support structure moving from the monopile to the jacket type under each load
combination. Maximum displacement occurs always for load case 6.1b giving rise to the higher
overturning moment; for the jacket type it is almost one-third the one of the monopile.
In Table 4 the applied loads and the numerical results obtained for the more severe
combination (6.1b) are reported, where the maximum stress in the tower has been computed
by the combination of compression (or tension) and bending stresses.
Table 4: Applied loads and the numerical results (loads combination 6.1b)
Actions
Reactions at
mud line
Structural
checks
Wind on rotor [KN]
Wind on tower [KN]
Wave and current [KN]
Overturning moment [KN*m]
Shear reaction at mud
line [KN]
Vertical reaction at mud
line [KN]
Maximum stress in the
tower [N/mm2]
Nacelle displacement [m]
Monopile
1663
740
3372
350456
5775
Tripod
1663
740
3372
350456
5775
Jacket
1663
428
3500
337087
5591
10714
286
10356.3
(max in pile
=15018)
230
13768
(max in pile
=9929)
151
4.66
3.72
1.82

19. 102
S TRUCTURAL D ESIGN
AND
A NALYSIS
OF
O FFSHORE W IND T URBINES
S YSTEM P OINT OF V IEW
FROM A
Figure 12: Detailed jacket support structure meso-level model.
From the previous results, it can be deduced that the jacket support type is the best choice
for what concerns the structural response under extreme loads (above all for the maximum
stress in the tower and for the nacelle displacement).
A meso-level model has been prepared for this type of support, after the exploration of a
number of tentative models (the model is shown in detail in Figure 12).
The meso-level model of the OWT structure is shown in Figure 13 (left part), while the right
part of Figure 13 shows the foundation medium (five substrates with different mechanical
characteristics), modeled using brick finite elements.
This level of detail allows the designer to investigate the internal state of stress for critical
parts (Figure 14). The connection between the tower (shell elements) and the jacket is
modeled using rigid beams elements (middle part of Figure 14). The meso-model is subjected
to the load case referred to as 6.1b in Table 3 (most severe); the result gives a nacelle
displacement equal to 2 m and a maximum stress in the tower equal to 178 MPa (at the jackettower connection). This is in good agreement with the result of the macro-level. The small
differences are probably related to the variation in the tower diameter (ranging from
5.0 meters at the tower base to 3.4 meters at the top) along the vertical direction and to the

20. W IND E NGINEERING VOLUME 34, N O . 1, 2010
103
Figure 13: Meso-level structural model of the jacket and corresponding deformed shape under static
aerodynamic and hydrodynamic loads.
Figure 14: Elastic internal state of stress at critical zones, jacket-tower connection and tower
thickness transition.
varying thickness of the tubular member at a fixed transition section (right part of Figure 14).
These features are properly reproduced in the meso-level model, while in the macro-level
model they are set equal to their maximum values.
5.3. Buckling Analysis
Another important aspect concerns the stability problem. A static incremental analysis has
been conducted in order to assess the buckling load; in this case, the hydrodynamic actions

21. S TRUCTURAL D ESIGN
104
AND
A NALYSIS
OF
O FFSHORE W IND T URBINES
S YSTEM P OINT OF V IEW
FROM A
Figure 15: Results of the buckling analysis.
have been schematized by using of single force acting on the jacket at the mean water level
(Figure 15).
The analysis gives a multiple of 1.17 for the extreme load case referred to as 6.1b in Table 3.
It is important to outline that the first buckling mode shows a local instability of the tower
tubular section, an effect that cannot be accounted for with the macro-models.
6. CONCLUSIONS
In this paper, the system approach has been proposed as a conceptual method for the design
of offshore wind turbine structures. In this sense, a structural system decomposition has been
performed, with a specific view on the structural analysis and performance. The presented
considerations aim at the organization of the framework for the basis of design of offshore
wind turbines, as a support to the decision making, with specific reference to the structural
safety, serviceability and reliability for the entire lifespan. Furthermore, numerical analyses
have been performed to compare the safety performance of three different support structure
types, generally adopted for a water depth lower than 50m: monopile, tripod and jacket
support structures. Extreme loads with a recurrence period of 100-years have been applied at
this stage of investigation.
Well-known analytical formulations have been summarized for correct characterization
of both the aerodynamic and hydrodynamic actions, whose contribution is crucial for
assessing the structural behavior. An early analysis has been carried out for the investigation
of the dynamic response for each one of the three support structures. Thus, the natural modes
of vibration have been determined in relation with the principal geometrical design
parameters. This is essential for avoiding the occurrence of resonance when the frequencies
of the external forces could excite the structure’s natural modes. A subsequent static analysis
has been carried out simulating three different load combinations as prescribed by
International Standards: the relative influence of aerodynamic and hydrodynamic loads has
been assessed, focusing on the resultant shear force and the overturning moment at the mud
line, and on the horizontal displacement at the hub height. This step is introductory for the
selection of the jacket structure as the appropriate support type.
Moreover, the internal state of stress under the abovementioned steady extreme loads has
been evaluated by means of two different levels of detail for the numerical models (macroand meso-level). The analyses have confirmed that macro-level model results can predict the
basic aspects of the structural response, yet the meso-level model provides an additional and
more detailed picture of the structural behavior due both to the major capabilities of the

22. W IND E NGINEERING VOLUME 34, N O . 1, 2010
105
adopted finite elements (shell and brick instead of beam elements) and to the higher
geometrical resolution of the models.
Finally, an incremental analysis has been carried out to assess the buckling load of the
examined offshore wind turbine: this occurs in the tower tubular section for a multiplier equal
to 1.17 for the more severe extreme loads.
Starting from the results presented here, future and more refined studies can take into
account for other relevant effects influencing the dynamic response of the structure (e.g.
scour, coupling with foundation medium, non-stationary loads, non-linear interactions etc.) by
performing transient analyses.
ACKNOWLEDGEMENTS
The present work has been developed within the Wi-POD Project (2008-2010) and other
research projects in the field of wind engineering, partially financed by the Italian Ministry for
Education, University and Research (MIUR). Fruitful discussions with Prof. Pier Giorgio
Malerba of the Politecnico di Milano, Prof. Marcello Ciampoli of the Sapienza – Università di
Roma, Professor Hui Li of the Harbin Institute of Technology and Dr. Ing. Gaetano Gaudiosi of
the OWEMES association are gratefully acknowledged. Finally, Prof. Jon McGowan is
acknowledged, for inspiring part of this work.
REFERENCES
[1]
Hau, E., Wind Turbines: Fundamentals, Technologies, Application, Economics, 2nd edn.,
Springer-Verlag Berlin, Heidelberg, 2006.
[2]
Breton, S.-P. and Moe, G., Status plans and technologies for offshore wind turbines in
Europe and North America, Renewable Energy, 2009, 34 (3), 646–654.
[3]
Bontempi, F., Basis of Design and expected Performances for the Messina Strait Bridge,
Proceedings of the International Conference on Bridge Engineering – Challenges in the
21st Century, Hong Kong, 1-3 November, 2006.
[4]
NASA (National Aeronautics and Space Administration), Systems Engineering
Handbook, 1995. Available online on 10/2009 at: www.nasa.gov.
[5]
Simon, H.A, The Sciences of the Artificial, The MIT Press, Cambridge, 1998.
[6]
Bontempi, F., Gkoumas, K. and Arangio, S., Systemic approach for the maintenance of
complex structural systems, Structure and infrastructure engineering, 2008, 4, 77–94.
[7]
[8]
Snel, H., Review of Aerodynamics for Wind Turbines, Wind Energy, 2003, 6 (3), 203–211.
Westgate, Z.J. and DeJong, J.T., Geotechnical Considerations for Offshore Wind
Turbines, 2005, Report for MTC OTC Project, Available online on 10/2009 at:
http://www.masstech.org/IS/Owec_pdfs/GeotechOffshoreFoundations-MTCOWC.pdf.
[9]
Ibsen, L. B. and Brincker R., Design of a New Foundation for Offshore Wind Turbines,
Proceedings of the IMAC-22: A Conference on Structural Dynamics, Michigan, 26–29
January, 2004.
[10]
Zaaijer, M. B., Foundation modelling to assess dynamic behaviour of offshore wind
turbines, Applied Ocean Research, 2006, 28 (1), 45–57.
[11]
Veldkamp, D., A probabilistic approach to wind turbine fatigue design, Proceedings of
the European wind energy conference and exhibition, Milan, 7–10 May, 2007.
[12]
Tempel, J. van der, Design of support structures for offshore wind turbines, PdD Thesis,
Technische Universiteit Delft, 2006.

23. 106
S TRUCTURAL D ESIGN
AND
A NALYSIS
OF
O FFSHORE W IND T URBINES
S YSTEM P OINT OF V IEW
FROM A
[13]
Biehl, F. and Lehmann, E., Collisions of Ships and Offshore Wind Turbines: Calculation
and Risk Evaluation, Proceedings of the International Conference on Offshore
Mechanics and Arctic Engineering, Hamburg, 4–9 June, 2006.
[14]
Martìnez, E., Sanz, F., Pellegrini, S., Jiménez, E. and Blanco, J., Life cycle assessment of a
multi-megawatt wind turbine, Renewable Energy, 2009, 34 (3), 667–673.
[15]
Weinzettel, J., Reenaas, M., Solli, C. and Hertwich, E.G., Life cycle assessment of a
floating offshore wind turbine, Renewable Energy, 2009, 34 (3), 742–747.
[16]
Sumur, B.M. and Fredsøe, J., The mechanics of scour in the marine environment, World
Scientific Publishing Co., Singapore, 2002.
[17]
Tempel, J. van der, Zaaijer, MB. and Subroto, H., The effects of scour on the design of
offshore wind turbines, Proceedings of the 3 rd International conference on marine
renewable energy, Blyth, July 6–9, 2004.
[18]
Henderson, A.R. and Patel, M.H., On the modeling of a floating Offshore Wind Turbines,
Wind Energy, 2003, 6 (1), 53–86.
[19]
Jonkman, J.M. and Buhl Jr., M.L., Loads Analysis of a Floating Offshore Wind Turbine
Using Fully Coupled Simulation, Proceedings of the WindPower Conference and
exhibition, Los Angeles: California, June 3–6, 2007.
[20]
API (American Petroleum Institute), Recommended Practice for Planning, Designing
and Constructing Fixed Offshore Platforms–Load and Resistance Factor Design (RP
2A-LRFD), 1993 (suppl. 1997).
[21]
BSH (Bundesamt für Seeschifffahrt und Hydrographie), Standard: Design of Offshore
Wind Turbines, 2007.
[22]
DNV (Det Norske Veritas), Offshore Standard: Design of Offshore Wind Turbine
Structures (DNV-OS-J101), 2004.
[23]
GL (Germanischer Lloyd) Wind Energie GmbH, Richtlinie zur Erstellung von
technischen Risikoanalysen für Offshore-Windparks, 2002.
[24]
GL (Germanischer Lloyd) Wind Energie GmbH, Guideline for the Certification of
Offshore Wind Turbines, 2005.
[25]
IEC (International Electrotechnical Commission), Wind Turbine Generator Systems –
part 3: Design requirements for offshore wind turbines (IEC 61400-3), 2009.
[26]
Bontempi, F., Li, H., Petrini, F. and Gkoumas, K., Basis of Design of Offshore Wind
Turbines by System Decomposition, Proceedings of the 4th International Conference on
Advances in Structural Engineering and Mechanics, Jeju, Korea, 26–28 May, 2008.
[27]
Starossek, U., Progressive Collapse of Structures, Thomas Telford Publishing, London,
2009.
[28]
Bontempi, F., Giuliani, L. and Gkoumas, K., Handling the exceptions: dependability of
systems and structural robustness, Proceedings of the 3rd International Conference on
Structural Engineering, Mechanics and Computation, Alphose Zingoni (Ed.), Millpress,
Rotterdam, 2007.
[29]
Polnikov, V.G., Manenti S., Study of relative role of nonlinearity and depth refraction in
wave spectrum evolution in shallow water, Journal of Engineering Applications of
Computational Fluid Mechanics, 2009, 3 (1), 42–55.

24. W IND E NGINEERING VOLUME 34, N O . 1, 2010
[30]
107
Bontempi, F., Li, H., Petrini, F. and Manenti, S., Numerical modeling for the analysis and
design of offshore wind turbines, Proceedings of the 4th International Conference on
Advances in Structural Engineering and Mechanics, Jeju, Korea, 26–28 May, 2008.
[31]
Petrini, F. Giuliano, F. and Bontempi, F., Comparison of time domain techniques for the
evaluation of the response and the stability in long span suspension bridges, Computer
& Structures, 2007, 85, 1032–1048.
[32]
Van Binh, L., Ishihara, T., Van Phuc, P. and Fujino, Y., A peak factor for non-Gaussian
response analysis of wind turbine tower, Journal of Wind Engineering and Industrial
Aerodynamics, 2008, 96 (10–11), 2217–2227.
[33]
Brebbia, C.A. and Walker Newnes, S., Dynamic analysis of offshore structures,
Butterworth, London, 1979.
[34]
www.vestas.com.