The complexity of the dynamic behaviour of offshore marine structures requires advanced simulations tools for the accurate assessment of the seakeeping behaviour of these devices. The aim of this work is to present a timedomain model for solving the dynamics of floating marine devices, subjected to nonlinear environmental loads and paying special attention on the mooring dynamics. First, the formulation of the hydrodynamic approach for solving the wavefloater interaction is introduced. Second, the solver of the mooring dynamics, based on a nonlinear Finite Element Method approach, is presented. Third, a procedure for coupling the hydrodynamic along with other external loads, with the floating structure and mooring dynamics is described. Fourth, some validation examples and comparisons among different mooring approaches are presented. Fifth, an analysis of the OC3 floating wind turbine concept is performed to study the influence of different mooring models, the effects of nonlinear waves on the platform, and the tension in the mooring system. The dynamic mooring model along with the secondorder wave model produce realistic simulations of the floating wind turbine performance.
Research trends in Marine Renewable Energies (MRE) are mainly focused in offshore wind energy due to the high expectations raised by this technology. The technology for marine wind turbines is currently welldeveloped, but limited for fixed installations in shallowwater areas. The next horizon is focused on deepwater technology [1], but different challenges for Floating Offshore Wind Turbines (FOWT) are not solved yet [2], such as the dynamic stability in the presence of nonlinear ambient loads [3]. In fact, an accurate prediction of the dynamic response of a FOWT, considering the interaction among the hydrodynamics, mooring, and aerodynamics of the turbine, is identified as one of the key challenges for the simulation tools required to design the future FOWTs [4,5,6].
Standard design procedures and simulation tools for marine structures come from the existing technology and experience of the offshore oil and gas industry. For instance, the classic simulation approaches are based on uncoupled formulations, where the hydrodynamic response of the floater is linearised and can be decoupled from the mooring [7,8]. Recently, coupled simulations have been adopted to solve the seakeeping of FOWT devices, since the dynamic of FOWT offers a high complexity due to the variety of loads and nonlinear effects. Anyhow, the interaction among different components, such as the wind turbine structure, the rotor dynamics, the mooring arrangements and the floating structure must be taken into account in a more accurate way [9,10].
The analysis of FOWT should be carried out with simulation codes capable to include the physics governing the dynamic response of these devices. With regards to marine structures, Low and Langley [11] showed that the dynamic response of a floating production system in a random sea can be split in two timescales: low frequency and wave frequency responses. Moreover the seakeeping of the floating device and the dynamics of the mooring lines are coupled. Then, the analysis should take into account the interaction between them, and the timedomain analysis seems to be the right way to simulate this sort of coupled problems. In fact, the American Bureau of Shipping [32] considers that the global seakeeping analysis of a FOWT should take into account: the unsteady wind loads, wind turbine control systems, wind turbineplatform interaction, wave actions over the platform, currents, mooring loads, and any other types of external actions. It will be presented later on that the timedomain approach allows to handle these actions in a natural manner.
The first works proposing coupled formulations for floating production systems were developed for TLPtype platforms [12,13,14], where it was found that the sumfrequency effects are important. Also other authors investigated and developed models to couple different effects and loads in floating devices [15,16,17,18]. More recently, Cordle and Jonkman [5] made a review of the state of art of the simulation tools for FOWT. Bae and Kim [9] recently presented a research on the effects of secondorder wave excitation in a monocolumnTLP type FOWT comparing with the uncoupled simulations in timedomain. Karimirad and Moan [19] developed a simplified method for the coupled dynamics of a offshore wind turbine aiming at saving computational time. They also analysed a spartype FOWT, and compared different hydroelasticity codes [2]. In [3], the dynamic response of the spartype platform subject to wave induced excitation was investigated numerically, including catenary mooring cables. Matha et al. [6] investigated a platformtower coupled with a TLPtype FOWT. Jonkman and Sclavounos [20] presented a tool integrating an aeroelastic model for onshore wind turbines, and a hydrodynamic load model, together with a QuasiStatic (QS) catenary model for mooring lines. More sophisticated mooring models, which are usually based on Finite Element Methods (FEM) have been investigated; for instance, Kim et al. [21] presented a comparison between a linear spring and a nonlinear FEM mooring for the analysis of the dynamic response when they are coupled with a floating structure. Several coupled seakeeping analyses with FEM mooring line models can also be found in the literature [22,23,24,25,26,27].
Frequencydomain and timedomain approaches are used for seakeeping analyses of marine structures. However, the frequencydomain approach has difficulties to accurately handle nonlinearities such as those arising from the mooring lines, and the low frequency components of the wavebody interaction, as appointed by Low [29], while the timedomain analysis can straightforwardly include any nonlinearity within each time step in a natural manner. However, the main drawback of the timedomain is an increase of the computational time required for the simulations. To overcome this limitation, Low and Langley [11] and Low [29] presented a hybrid timefrequency domain model to simulate low and wave frequency response of coupled problems.
In this work, an extension of the timedomain method proposed by ServánCamas and GarcíaEspinosa [30,31] is used. This method obtains a relevant reduction of the computational time thanks to the use of deflation techniques and High Performance Computation based on Graphical Processor Units (GPU). The tool is based on the Finite Element Method (FEM) and is able to solve multibody seakeeping problems on unstructured meshes including any type of external load. Other examples of FEM solvers for seakeeping analysis can be found in the literature. For instance, Hong and Nam [33], who presented a secondorder analysis of wave forces using FEM in the timedomain, and investigated the interactions with multibody devices.
This work presents the development of a coupled FEM seakeeping and mooring models for the analysis of floating offshore structures. The model is able to take into account first and the secondorder irregular waves, wind loads, and mooring loads. A novel iterative scheme for coupling the wave diffractionradiation solver developed by ServánCamas and GarcíaEspinosa [28,30,31] with nonlinear aerodynamics and mooring loads is also described. The paper is organized as follows. First, the governing equations of the body dynamics are introduced. Second, the secondorder diffractionradiation wave problem is described. Third, the nonlinear FEM model for mooring lines is introduced in detailed. Fourth, the coupling between the dynamics of the floater with nonlinear loads, such as mooring lines forces, is explained. Fifth, some validations with experimental results are shown, as well as a comparison of the nonlinear FEM model with the QuasiStatic catenary model. Sixth, we analyse an operational case of a spar buoy FOWT based on the OC3 concept and NREL 5 MW turbine. This case study aims at evaluating the influence of the type of mooring model, as well as the effects of nonlinear wave on the dynamics of the platform. Finally, some relevant conclusions from the obtained results are presented.
The motion of a floater subject to ambient loads can be modelled using the rigid body dynamics. Let OXYZ be a fixed global frame of reference, and let Gxyz be a local frame of reference located at the center of gravity, and whose axis are parallel to the axis of the global frame (see Fig. 1). Assuming small rotations, for each time step, the body accelerations can be obtained respect to the local frame from the rigidbody dynamic equations:

where is the mass matrix, is the linear acceleration vector , is the instantaneous inertia tensor, and are the external loads vector (hydrostatics, wave loading, mooring, wind, etc.) and the external moments respectively; finally is the angular acceleration vector.
Figure 1: Global and local frame of reference used in computation of floater dynamics. 
The calculation of the external forces over the body constitutes an essential part of the dynamics, and will be described in more detailed later on.
Assuming incompressible and irrotational flow in a domain , being the wetted surface of the floating device, the wave problem governing equations are [28]:

where is the velocity potential, is the free surface elevation, is the gravity acceleration, is the pressure on free surface, is the fluid density, is the wave elevation, is a pressure at a point over body, is the fluid velocity, is the local velocity at a point on the wetted body surface, is the vector normal to the body wetted surface (pointing upward this surface), and is the vertical coordinate of any point of the body.
The governing equations for the secondorder diffractionradiation wave problem are obtained applying Taylor expansion on the boundary surfaces of a timeindependent domain. This approach allows to approximate the free surface on and the mean body surface at time . Then, a perturbed solutions based on Stokes expansion procedure is applied to the velocity potential, free surface elevation, and body motion. More details can be found in [28].
The solution can be decomposed as

where is the incident wave velocity potential, is the diffractionradiation wave velocity potential, is the incident wave elevation, and is the diffractionradiation wave elevation. Then, the wave diffractionradiation governing equations up to secondorder are [28]:

where superscripts 1 and denote the components at the firstorder and up to secondorder solution, and is the displacement vector at a point over body.
With regards to the ambient loads applied over wetted body surface, hydrodynamic wave forces and moments can be obtained directly from pressure integration over the wetted body surface. Thus, it can be written that

where subscript denotes the hydrostatic loads and denotes the dynamic loads. and are the initial hydrostatic forces and moments over the body, and are the up to secondorder hydrostatic loads and moments, and and are the up to secondorder dynamic loads and moments. Details of each component can be found in [28].
The dynamic equations for a mooring cable with length with negligible bending and torsional stiffness can be formulated as [34,35]

(17) 
where is the water density, is the added mass coefficient, is the mass per unit length of the unstretched cable, is the position vector, is the Young's modulus, is the crosssectional area of the cable, is the strain, are the external loads applied on the cable, and is the length along the unstretched cable.
The boundary conditions are given by

where is the second derivative of the position vector at the fairlead connection point. The external loads acting on the cable, considered in this work, are the selfweight of the cable, hydrostatic loads, drag forces [36], and seabed interaction.
When the cable undergoes an excitation, the part which lies between the anchor and the touchdown point interacts with the seabed. This interaction is a complex nonlinear effect. In this work, the seabedmooring interaction is modelled as a springdamping system [37,38], and is implemented as follows:

(21) 
where is a coefficient limiting the seabed reactions, is the portion of the cable resting on the seabed, is the weight per unit of length of the line, is the apparent weight of the cable, is the term related to the numerical integration of the dynamic FEM model, is the vertical coordinate of the cable, is the seabed stiffness, is the contact area of the line, and is the time step. The term is defined as

(22) 
where is the diameter of line.
The term can be defined as a limit of the line subsidence.

being a term related to the numerical scheme adopted. In addition is expressed as

(25) 
where is the seabed damping Palm.

(26) 

(27) 
The algorithm developed to solve the mooring dynamics is described next.
Truss elements, with just three translational degrees of freedom per node, are used for modelling the mooring lines, since bending effects can be neglected in most of cases [7,40]. In this work, a FEM approach combined with an updated Lagrange formulation is used for describing the dynamics of the mooring cable. Some authors showed that the corotational formulation can get a better performance than the updated formulation. However some instabilities and lack of convergence can appear. Figure 2 shows a scheme of the discretization adopted in this work.
Figure 2: Scheme showing the general approach adopted for the spatial discretization of the cable mooring. 
Applying the standard FEM formulation for the nonlinear elastodynamics problems [41], the equations for the dynamic equilibrium of the forces on a cable for each time step can be written as

(28) 
where are the external loads vector, is a consistent mass matrix of the line, considering inertia and added mass, is the pretension vector in the initial configuration, and is the internal forces vector of the cable. Damping effects of the mooring cable are introduced through a Rayleigh proportional damping matrix of . The application of the nonlinear FEM approach to the cable equation can be found in [41,42].
Considering the linearization of the current configuration, Eq. (28) can be expressed as

(29) 
where and are called the material stiffness matrix and the geometric stiffness matrix, respectively, in the FEM literature [41,42]. The sum of both matrices is the socalled tangent stiffness matrix. The geometric part of the stiffness matrix is considered as nonlinear since no material properties appear, and it depends of the SecondPiola stress tensor of the current configuration. Incremental displacement of the cable nodes is .
An implicit BossakNewmark [43] time integration scheme is applied for the timeintegration of the Eq. (29). This provides a set of algebraic equations to be solved iteratively,

where is the time step, denotes the ith iteration, is a parameter concerned with the BossakNewmark implicit method, and and are parameters related to the Newmark time integration scheme.
The new position and velocity of each node in each time step can be expressed as (see Fig. 3)

It can be highlighted that multisegmented mooring systems can be solved with this approach, and the equilibrium between two or more mooring cables is determined using the NewtonRaphson method. A criterion based on the maximum difference between the position reached by the nodes in two consecutive iterations is applied to evaluate the convergence of the algorithm.
Figure 3: General approach to algorithm for solving the floater dynamics. 
The iterative procedure for solving the cable dynamics can be summarized as
Most of the models found in the literature to solve the coupled mooringbody dynamics use a frequency domain analysis of the floater together with a convolution integral [46] for solving the motions of the coupled system [9,20,19]. The most common approach is based on a frequencydomain diffractionradiation solver based on the Boundary Element Method (BEM) combined with a FEM model to solve the mooring dynamics. In this work, a different approach based on a timedomain FEM seakeeping model recently presented [30,31] is proposed. This approach allows to straightforwardly couple the seakeeping of the floater with nonlinear loads.
The algorithm used in this work to solve the dynamics of the coupled system is presented in Fig. 3. In order to accelerate the solution of the nonlinear solver, it includes two nested loops; the external loop iterates on the wave diffractionradiation problem, while the internal loop takes into account the remaining external forces vector acting on the body. In this figure are the external forces different from the hydrodynamic and the mooring forces, and is the matrix of the linearised mooring. The procedure to carry out the coupled analysis is as follows:

(33) 
where is the restoring force vector of the mooring cables.
As mentioned above, the cable dynamics is formulated in term of the acceleration, and this is also valid for the boundary condition of the fairlead connection point. A linear approximation to evaluate the end node acceleration based on the prescribed displacement is proposed in this work. Each time step is divided in subinterval, that is to say, . So, in the th time step, the acceleration of end node fulfills the following compatibility relationship

(34) 
where is a coefficient to be determined in each time step. Applying an appropriate boundary condition, this coefficient can be formulated as

(35) 
Above formulation for the boundary condition at the fairlead point has shown a better stability for the dynamics solver than higher order approximations.
As it was presented in the previous section, in the first iteration of the dynamic loop, the stiffness matrix of the cable is estimated by obtaining the Jacobian of the reaction forces using numerical differentiation,

(36) 
where is the reaction of the mooring cable at the fairlead point. Thus, the cable response is linearised within each time step , by estimating the mooring restoring forces as

where the terms correspond to a linear stiffness matrix, and , and are the displacements of the fairlead point from the position at the beginning of the current time step.
In this section some validation examples of the nonlinear FEM model are presented.
The first case is based on that presented in [47]. It consists of an isolated cable, with fixed ends, subjected to its own weight (see Fig. 4). Initially the cable has a flat form. The expected deformation is a U form, and the reactions at the ends must be equal to the cable weight. The properties of the cable are: the stiffness 50 N, the weight per unit length N/m, and m of span length. The cable is discretized into twentytwo bar elements, and the time step adopted is s. Figure 5 shows different positions of the cable until it gets the expected U form. Note that a damping increment leads to a faster convergence of the stationary solution. The reactions at end points are , and the maximum deflection (0.715 m) is reached at m.
Figure 4: Validation of the nonlinear FEM mooring model. Case 1: cable under its self weight. 
Figure 5: Validation of the nonlinear FEM mooring model. Case 1: different stages of time evolution of cable under its self weight. 
The Ms Excel file below includes the results of the time evolution of the cable under its self weight (corresponding to Figure 5).
Case_1.xlsx
The second case is based on that proposed by [48]. The experiment consists of a cable initially in a horizontal position, and letting one end free and leaving the cable evolve under gravitational loads. The computed results are compared with the experimental results taken from [48], as well as with the data obtained from simulation with the FEM structural solver RamSeries (www.compassis.com). The properties of the cable are: length m, stiffness 50 N, weight per unit of length N/m, and m distance between the cable end points. The cable was divided into forty four bar elements, and the time step adopted was s. This time step must be low enough for obtaining an accurate description of the cable motion. The obtained numerical results show a good agreement between our results, and those experimentally and numerically obtained by other authors. The cable position at different times obtained from computed results can be observed in Fig. 6.
Figure 6: Validation of the nonlinear FEM mooring model. Case 2: different time step positions of free vibration cable obtained from computed results. 
Figure 7: Validation of the nonlinear FEM mooring model. Case 2: comparison between computed results of the path of free end of the cable obtained and experimental results of [48] and numerical computed with RamSeries. 
Slight differences can be appreciated at the lower end in Fig. 7. This fact can be explained by the different numerical parameters chosen to carry out the simulation.
The Ms Excel file below includes the results of the time evolution of the free vibration cable (corresponding to figures 6, 7).
Case_2.xlsx
Now, results obtained by the developed FEM solver are compared for the model test proposed by Lindhal and Sjoberg [38,39]. The experimental set up is shown in Fig. 8. The lower end was attached to the concrete floor and the upper end was attached to a circular plate with a fixed rotation speed. The radius of the circular motion was m. Two cases with different rotational periods of = 1.25 s and s respectively, were investigated. The reaction forces at the top end of the cable are measured and compared with those computed by the proposed numerical model.
Figure 8: Validation of the nonlinear FEM mooring model. Case 3: the geometrical setup of the experimental tests by [38]. 
Figure 9: Validation of the nonlinear FEM mooring model. Case 3: comparison between the experimental and numerical cable top end reaction forces. Rotational period = 3.5 s. 
The properties of the cable are: length m, stiffness N, weight per unit length N/m, and diameter m. In this validation case, the cable is discretized into 200 bar elements, and the time step adopted is s. The motion of the top end is defined by the following expressions (including an initialization period to build up the spinning of the plate):

The results are compared with the experimental results taken from [38]. A good agreement between the computed reaction forces and the experimental results [38] can be observed in Fig. 9 (for s), and 10 (for s) for both, the maximum values and the time evolution. Only slight differences are appreciated due to the uncertainty of the experimental data. The entire cable loses stiffness at some instants in time, and the numerical oscillations after the slack are larger in the case of the larger excitation frequency, as it was observed by [39].
Figure 10: Validation of the nonlinear FEM mooring model. Case 3: comparison between the experimental and numerical cable top end reaction forces. Rotational period = 1.25 s. 
The Ms Excel file below includes the results of the circular rotating plate case (corresponding to figures 9, 10).
Case_3.xlsx
A fully coupled analysis of the OC3 spar buoy offshore wind turbine, called Hywind (www.ieawind.org/task23/) is presented next. Main particulars of the spar buoy FOWT are presented in [52,53]. A general view of the buoy concept can be observed in Fig. 11. In this section, several analysis are made:
Figure 11: General view of the spar buoy wind turbine concept (OC3Hywind concept). 
First, a RAO analysis is performed in the absence of wind. The frequency results of the seakeeping solver are obtained after applying a Fourier transform to the time history generated. Figure 12 shows an intercode comparison. Note that a good agreement among the different solvers is found [49].
Figure 12: OC3Hywind concept. Comparison between the computed result by SeaFEM with those taken from other authors [49] for a rigid wind turbine with no wind. 
The Ms Excel file below includes the RAO curves obtained in the present work and the data from HydroDyn and WAMIT used as reference (see Figure 12).
RAOS.xlsx
Below, the influence of three different mooring models on the OC3 spar buoy FOWT is analysed. These models are: the linear model cable (that behaves as springs and is represented by a linearised mooring matrix [53]); the QuasiStatic model, similar to the one presented in [54]; and the dynamic model developed in this work. Six firstorder monochromatic waves are used in the analysis. Key parameters of the mooring layout and cable properties can be found in Table 1. Fig. 13 compares the pitch motion for each mooring model.
Item  Value  Unit 
Wave Amplitude  1.0  m 
Wave Period analysed  10; 25; 20; 35; 40; 55  s 
Number of Mooring Lines  3  
Angle Between Adjacent Lines  120  deg 
Depth to Anchors Below SWL  320  m 
Depth to Fairleads Below SWL  70  m 
Radius to Fairleads from Platform Centerline  853.9  m 
Unstretched Mooring Line Length  902.2  m 
Mooring Line Diameter  0.9  m 
Mooring Line Mass Density  77.71  kg/m 
Mooring Line Extensional Stiffness  3.8410  N 
It can be observed that there are big differences in the results in those cases close to the pitch resonance (about 30 s), while the results are quite similar for the cases with 10 s and 55 s. These results suggest that the use of simpler mooring models can lead to big errors near the resonance frequency, and as a consequence to magnify safety factors, contributing to increase the cost of the FOWT.
Finally, four analyses of the OC3 spar buoy in operational conditions are presented. The different analyses are carried out in similar environmental conditions, but using first and secondorder irregular waves. Furthermore, additional studies including QuasiStatic and dynamic mooring models are performed. The goal of these analyses is to evaluate the effects of the mooring model and the wave order on the dynamics of the system, as well as to estimate the tension in the mooring lines. On the one hand, the wind turbine system is assumed to be operating at an average wind speed of 11.4 m/s, which generates the maximum thrust and torque. FASTLognoter [50,51] has been used to linearise with FAST [50] the behaviour of the wind turbine around the operating wind speed. Restoration and damping matrices resulting from the linearisation of the wind turbine system are included into the global dynamics. It should be remarked that the rotational and periodicity effects are considered in the calculation of the steady state matrix. On the other hand, the wind loads are estimated considering nonuniform wind flow, with an average wind speed of 11.4 m/s. The wind flow profile is obtained using Turbsim [55], and the wind loads on the wind turbine are obtained from FAST/AeroDyn [50].
Case 1  Case 2  Case 3  Case 4  
Average Wind velocity  (m/s)  11.4  11.4  11.4  11.4  
Wind direction  (deg)  0.0  0.0  0.0  0.0  
Wave Spectrum  ()  JONSWAP 1  JONSWAP 1  JONSWAP 2  JONSWAP 2  
Significant wave height  (m)  6.0  6.0  6.0  6.0  
Peak period  (s)  12.0  12.0  12.0  12.0  
Mean wave direction  (deg)  0  0  0  0  
Mooring model  ()  Quasistatic  Nonlinear  Quasistatic  Nonlinear  
Number of mooring lines  ()  3  3  3  3  
Mooring lines elements  ()  200  200  50  200 
A JONSWAP spectrum with a mean wave period = 12.0 s, and significant wave height = 6.0 m, is simulated. The key parameters of the different case studies are presented in Table 2. As stated above, two different types of mooring models are analysed; one based on the QuasiStatic catenary model [54], and the other based on the dynamic (NFEM) cable model, presented in this work. For the dynamic cable analysis each mooring line is divided into 200 bar elements.
Figures 14, 15 and 16 show the computed heave, roll and pitch motions from 600 s to 900 s of simulation time. Noticeable differences are found between the first and the secondorder movements, while the QS and NFEM mooring models offer quite similar results.
Figure 13: Results obtained for mooring analysis around pitch resonance of OC3Hywind. 
Table 3 shows the mean and RMS values, as well as the motion amplitude for the first and secondorder movements. When comparing the QS and the NFEM models, only slight differences are observed. In particular, the secondorder pitch motion is higher when using the NFEM model, compared to the QS model, while the other values remain with similar trends for both models.
Case 1  
Surge (m)  Sway (m)  Heave (m)  Roll (deg)  Pitch (deg)  Yaw (deg)  
Mean 1  0.04  0.00  0.00  0.29  0.41  0.21 
Mean 1  0.04  0.00  0.00  0.29  0.41  0.21 
Amplitude 1  14.96  1.34  2.75  1.91  6.12  10.38 
Amplitude 2  14.96  1.34  2.75  1.91  6.12  10.38 
RMS 1  2.76  0.21  0.53  0.52  1.09  1.92 
RMS 2  2.73  0.24  0.45  0.48  1.22  1.91 
Case 2  
Surge (m)  Sway (m)  Heave (m)  Roll (deg)  Pitch (deg)  Yaw (deg)  
Mean 1  0.00  0.00  0.01  0.29  0.40  0.21 
Mean 1  0.10  0.00  0.03  0.30  0.42  0.28 
Amplitude 1  13.82  1.12  2.61  1.92  6.03  10.31 
Amplitude 2  15.19  1.55  2.59  2.02  8.00  10.83 
RMS 1  2.54  0.18  0.50  0.52  1.09  1.92 
RMS 2  2.73  0.24  0.45  0.48  1.22  1.91 
Next, a video of the analysis case 1 is presented.
Video 1. OC3 spar buoy wind turbine simulation (analysis case 1). 
Figure 17 shows the tension for each mooring line at the fairlead point. The NFEM model recorded larger amplitude oscillations (in the range of 5 s to 10 s period) compared with QS model. The differences observed in Fig. 17 in the tension amplitude reach up to 24 . This fact suggests that using a QS model for fatigue assessment of the mooring lines could overestimate their fatigue life.
Figure 14: Comparison between heave motion for first and secondorder wave environment for Case 14 (described in Table 2). 
Figure 15: Comparison between roll motion for first and secondorder wave environment for Case 14 (described in Table 2). 
Figure 16: Comparison between pitch motion for first and secondorder wave environment for Case 14 (described in Table 2). 
Figure 17: Comparison of fairlead tension of each mooring line for Case 3, and 4. 
Table 4 compares the maximum, minimum, average, and RMS tension values at the fairlead points, obtaining similar values for both mooring models. Furthermore, based on Figure 17, the secondorder simulation provided larger tension values than the firstorder. This result suggests that a firstorder approximation can underestimate the fatigue loads and might lead to a wrong mooring design.
Line  Case  Max. (N)  Min. (N)  Mean (N)  RMS (N) 
Line 1  1  1.43510  1.07310  1.25010  1.25210 
Line 2  1  1.44610  1.07210  1.24010  1.24210 
Line 3  1  7.41110  5.20910  5.99110  6.00310 
Line 1  2  1.45710  1.05210  1.24610  1.24810 
Line 2  2  1.47110  1.04010  1.23610  1.23810 
Line 3  2  7.42110  4.51010  5.92310  5.93610 
It is emphasized that the NFEM mooring model allows to consider nonlinear dynamic effects which cannot be taken into account by QS models. However, in deep water, the dynamics of catenary mooring lines are negligible as reported in Low.
A FEM coupled seakeeping and mooring model for the analysis of floating wind turbines is presented. Based on the results obtained in this work, the following conclusions are made:
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Published on 01/01/2016
DOI: 10.1016/j.marstruc.2016.05.002
Licence: CC BYNCSA license
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