Time Domain Global Dynamic Analysis and Load Generation Methodology for Floating Offshore Wind Turbine Substructures
Article information
Abstract
Ensuring the structural reliability of floating offshore wind turbine (FOWT) substructures requires global dynamic analysis methods that can accurately capture the combined effects of wind, waves, and currents. On the other hand, conventional integrated analysis tools focus primarily on global motions and are limited in their ability to represent structural responses. This paper presents a time-domain global analysis procedure and load-generation methodology that enable detailed finite-element structural analysis of FOWT platforms. The hydrodynamic coefficients were calculated using KR3D based on potential theory and incorporated into OpenFAST to perform fully coupled aero-hydro-elastic simulations under design loading conditions. The simulation results provided the basis for reconstructing all major time-domain load components, including tower-base loads, mooring tensions, inertial forces, wave pressures, and internal pressures. These loads are generated using coordinate transformations, transfer functions, and motion-based formulations. The reconstructed loads show strong agreement with the corresponding global dynamic results in terms of the amplitude and phase. Structural response analyses further showed that the applied loads produce physically consistent deformation patterns and stress distributions across critical structural regions. The proposed methodology enhances time-domain structural evaluation while efficiently linking global dynamic analysis.
1. Introduction
The global offshore wind industry is rapidly expanding as turbine capacities increase and development extends into deeper waters. This trend has established an urgent need for reliable structural analysis methodologies for floating offshore wind turbine (FOWT) substructures. Floating platforms are continuously exposed to complex environmental forces generated by wind, waves, and currents. These forces interact in a nonlinear and highly coupled manner, producing intricate global motions and significant time-varying internal loads. As a result, an accurate prediction of the structural reliability of floating platforms requires analysis techniques that can adequately capture the combined aero-hydro-servo-elastic behavior in the time domain. International design standards such as DNV-ST-0119 and IEC 61400-3-2 highlight the importance of comprehensive global dynamic analyses and systematic evaluation of multiple design load cases. Nevertheless, most widely used integrated simulation tools, including OpenFAST, OrcaFlex, and BLADED, model the floating platform primarily as a rigid body. These models are effective for predicting global platform motions and turbine system dynamics, but they provide limited insight into localized structural responses such as sectional loads, pressure distributions, and stress concentrations. As a result, structural assessments often rely on simplified assumptions or incomplete load-transfer procedures, which may compromise the accuracy of ultimate limit state (ULS) and fatigue limit state (FLS) evaluations.
Several studies have attempted to address this challenge. Han et al. (2018) proposed a load transfer approach that links coupled dynamic simulations with structural solvers. Yu and Shin (2020) performed time-domain coupled dynamic analysis of an MW-class floating offshore wind turbine based on IEC 61400-3-2. Cho et al. (2021) generated fully coupled nonlinear time-domain simulation data of a spar-type floating wind turbine and applied them to fault classification of the blade pitch system. Kim et al. (2022) conducted time-domain motion analysis of a combined TLP-type floating offshore wind turbine and wave energy converter under wave-induced loads, including second-order wave effects. Gao et al. (2023) synthesized radiation, diffraction, and hydrostatic pressures using hydrodynamic transfer functions and validated the resulting stress predictions. Wang et al. (2023) examined the dynamic response of a semi-submersible hull supporting a 10 MW turbine and stressed the importance of linking global dynamic analysis with localized stress evaluation. Wang and Moan (2023) proposed a methodology for load-effect analysis and ultimate limit-state design for semi-submersible hulls, highlighting the need for physically consistent decomposition of hydrodynamic and aerodynamic loads. Li et al. (2024) developed an integrated global design method that incorporates hydrodynamic loads, operational conditions, and structural considerations, highlighting the importance of unified global local workflows. Kim et al. (2025) also reported the relevance of time-domain structural evaluations through a buckling assessment of a 15 MW substructure using FLOW Stress. Despite these advances, significant challenges remain. Many methods struggle to preserve phase information during load reconstruction or fail to maintain equilibrium when combining load components derived from different simulation modules. In some cases, dynamic pressure contributions from internal ballast fluids or fluctuating hydrostatic components are simplified or ignored, leading to an underestimation of local stresses and inaccuracies in structural performance assessment.
To address these gaps, the present study proposes an integrated time-domain load-generation methodology that reconstructs all major load components required for the structural analysis of semi-submersible FOWT platforms. The approach begins with hydrodynamic coefficients calculated by KR3D, which are incorporated into OpenFAST to perform fully coupled aero-hydro-servo-elastic simulations. The radiation and diffraction pressures, hydrostatic restoring pressures, tower base loads, mooring line tensions, and inertia-induced internal pressures are reconstructed in a form suitable for finite element analysis based on the resulting motion and load histories. The methodology emphasizes preserving phase relationships, ensuring consistent global equilibrium, and enabling element-wise load mapping. This integrated load-generation framework enhances the connection between global load simulation and structural evaluation. It provides a flexible, physics-based foundation for a time-domain evaluation of ultimate and fatigue limit states, thereby improving the design reliability of next-generation floating wind platforms.
2. Procedures
This section describes the global dynamic analysis procedure used to obtain platform motions and environmental load components, which serve as the basis for the load-generation methodology presented in this study. The hydrodynamic coefficients were first calculated using the potential solver KR3D and subsequently integrated into the fully coupled aero-hydro-servo-elastic framework of OpenFAST. The following subsections summarize the system configuration and simulation setup.
2.1 Analysis Model
The model consists of the International Energy Agency (IEA) 15 MW reference wind turbine mounted on a three-column semi-submersible platform. Table 1 lists the turbine parameters, including the hub height and rotor diameter. The semi-submersible hull comprises three circular columns connected by pontoons arranged in a triangular configuration. The structure includes a central tower support column and three outer columns providing buoyancy and stability. Table 2 lists the principal geometric and hydrostatic characteristics of the platform, including the draft, center of buoyancy, waterplane area, displacement, and metacentric height. Mooring stability is achieved using three catenary chain lines arranged at 120° intervals around the platform. The hydrodynamic characteristics of the platform were generated using KR3D based on potential flow theory. The computed added mass, radiation damping, and wave excitation coefficients were provided as frequency-dependent datasets and incorporated into OpenFAST through its HydroDyn module. The simulations were performed under a normal turbulence model (NTM) wind conditions and JONSWAP irregular waves to represent realistic design sea states.
Main features of the IEA 15 MW wind turbine
Main features of a semi-submersible platform for the IEA 15 MW wind turbine
2.2 Analysis Procedure
The overall analysis procedure adopted in this study integrates the hydrodynamic computation, fully coupled aero-hydro-servo-elastic simulation, time domain load generation, and finite element (FE) analysis into a coherent workflow, as shown in Fig. 1. The procedure establishes a direct interface between global dynamic simulations and detailed structural evaluation by reconstructing all relevant load components into a form suitable for FE application. The process began by calculating the frequency-domain hydrodynamic coefficients for the semi-submersible platform using KR3D. These coefficients included the added mass, radiation damping, wave excitation forces, and hydrostatic restoring terms, which provided the fundamental hydrodynamic inputs for the time-domain simulations. The calculated data were then incorporated into OpenFAST through the HydroDyn module to perform fully coupled aero-hydro-servo-elastic simulations under the selected design load case (DLC 1.6). From the OpenFAST simulations, time histories of platform motions, tower base loads, and mooring line tensions are extracted. These outputs served as the primary inputs for the load generation module. Based on these results, the external loads acting on the floating structure were reconstructed following the step-by-step procedure summarized below:
Analysis procedure
(1) Extraction of global responses
Time series of rigid body motions, accelerations, tower base loads, and mooring tensions were obtained from OpenFAST in the global inertial coordinate system.
(2) Coordinate transformation
All force and moment components were transformed into the body-fixed coordinate system of the floating platform using the instantaneous rotation matrices based on the roll, pitch, and yaw motions.
(3) Reconstruction of the wave-induced pressures
Radiation and diffraction-induced pressures were reconstructed in the time domain by combining the frequency domain pressure transfer functions (Hi(ω)) obtained from KR3D with the Fourier-transformed motion and wave elevation signals. The pressure acting on the structural panel (1) is expressed as Eq. (1):
where F and F−1 denote the Fourier and inverse Fourier transform, respectively.
(4) Calculation of inertia-induced and hydrostatic pressures
The inertia forces associated with structural mass and internal ballast water were evaluated from platform accelerations, while the time-varying hydrostatic pressures were calculated from the instantaneous heave, roll, and pitch motions using kinematic formulations. These pressures were distributed to the corresponding internal and external panels of the FE model.
(5) Assembly and mapping of loads to the FE model
All reconstructed pressures and concentrated forces were mapped onto the FE structural model at the element and nodal levels, considering the local geometry, panel areas, and orientation vectors. This step produced the time histories of nodal forces and element pressures directly applicable to the FE solver.
(6) Structural analysis
The assembled load sets were applied to the FE model to calculate time domain structural responses, including stress distributions and deformation patterns.
The phase consistency among all load components is ensured by reconstructing every load using the same platform motion and wave time series and by adopting identical frequency grids and fast Fourier transform (FFT) / inverse fast Fourier transform (IFFT) procedures for all frequency-to-time conversions. As a result, all reconstructed loads share a common time base and phase reference, which is essential for preserving the coupled dynamic characteristics of the floating system. Furthermore, the reconstructed loads must satisfy the global equilibrium at each time step. The sum of all applied external loads in the body fixed coordinate system was verified against the inertia forces derived from platform accelerations, ensuring physical consistency before the loads are transferred to the structural model. Through this procedure, Fig. 1 provides a high-level overview of the analysis flow and the detailed interface between global dynamic simulation, load generation, and finite-element structural analysis, enabling systematic and reproducible time-domain structural evaluation of floating offshore wind turbine substructures. Table 3 lists the design-load cases, and Fig. 2 shows an illustration example of an OpenFAST simulation.
Design load cases (DLC 1.6 from IEC 61400-3-2)
Illustration example of an OpenFAST simulation
3. Generation of the Loading Components
The external loads acting on the floating structure obtained from the global dynamic analysis are defined as external forces, and the sum of all external forces must be equal to the inertia forces of the floating body, as expressed in Eq. (2). Hence, the global dynamic equilibrium of the system requires that all environmental, hydrodynamic, aerodynamic, and mooring related forces collectively match the instantaneous inertia of the structure.
The external forces can be decomposed into static and dynamic components to describe this relationship more explicitly, as expressed in Eq. (3). The static component primarily consists of gravity and buoyancy, which remain relatively constant during the simulation, apart from variations due to platform motion. The dynamic component includes the loads generated by the wind turbine and tower, mooring line forces, and wave-induced pressures. The total weight of the floating structure must also be represented appropriately for load calculations. In Eq. (4), the total weight is divided into the structural weight of the substructure and the weight of the internal ballast water. This separation is important because the ballast water behaves dynamically owing to the relative motion of the platform, thereby contributing to the static weight, the internal pressure distribution, and the inertia forces within the floating body. Distinguishing between structural mass and ballast mass enables more accurate evaluation of pressure fields, internal fluid motion, and inertia-related loading effects.
As an illustrative example, the probability level P can be calculated as the ratio that relates the recurrence interval to the expected maximum value of the environmental load when a given design load case (DLC) corresponds to a recurrence period of N years and the associated sea state duration is defined as hours. This probability level is used to evaluate the extreme responses or statistically representative loads for a specific return period. This framework provides a direct connection between environmental statistics and the structural loads used in the simulation:
3.1 Tower Base Load
The thrust force generated by the rotor and the loads transmitted through the rotor nacelle assembly (RNA) were provided by OpenFAST at the tower-base reference point as time-varying forces and moments, as shown in Fig. 3. These tower base loads represent the combined effects of aerodynamic excitation, turbine control actions, and the dynamic deformation of the blades and tower. Therefore, they capture an essential portion of the coupled turbine platform interaction. The loads must be transformed into the body-fixed coordinate system of the floating platform before being applied to the structural model because OpenFAST outputs the tower base loads in the global inertial frame. This transformation is performed through rigid body elements (RBEs), which transfer the loads from the tower base reference point to the corresponding nodes in the finite element model.
Example of tower-base force
Accurate reconstruction and application of tower-base loads are critical because aerodynamic thrust and the associated overturning moments strongly influence the platform pitch response and global equilibrium. Proper representation of these loads ensures that the global dynamic behavior and the local structural responses around the tower support region are reproduced realistically in the time-domain structural analysis.
3.2 Mooring Force
The mooring line forces obtained from OpenFAST are provided in the global inertial coordinate system. They must be transformed into the body-fixed coordinate system of the floating platform before they can be applied to the structural model, as shown in Fig.4. This transformation is performed using the rotation matrix defined in Eq. (5), which accounts for the instantaneous roll, pitch, and yaw motions of the platform. The fairlead-level loading captures the restoring characteristics of the mooring system and directly influences the global surge, sway, and yaw responses of the platform. Therefore, accurate application of these transformed forces is essential for reproducing the correct global equilibrium behavior and for ensuring that the structural model reflects the true interaction between platform motion and mooring line tension. Here, θ1, θ2 and θ3 denote the roll, pitch, and yaw angles, respectively.
Example of the mooring force
3.3 Inertia Force
Platform accelerations generate the inertia forces associated with the structural mass of the floating body and the mass of the internal ballast water. These inertia forces contribute to the global equilibrium of the platform and must be included as part of the external loading applied to the structural model. The internal ballast water also produces a dynamic pressure field that varies with platform acceleration and the relative position within each tank. This pressure distribution is calculated using Eq. (6) and applied to the corresponding tank panels during structural analysis. Proper representation of these inertia-induced pressures is essential because they influence the local stress response and the global motion characteristics of the floating platform. Here, ρ is the density of ballast water and ax, ay, and az denote the tank acceleration in the longitudinal, transverse, and vertical directions, respectively:
The inertia-induced pressures were evaluated in the body-fixed coordinate system with the origin at the platform center of gravity. The translational accelerations obtained from the global dynamic simulation were used to calculate the local pressure field in each ballast tank, while the contribution of angular acceleration terms is neglected in the present study because of its relatively small influence.
3.4 Time Varying Static Pressure
The relative heave, roll, and pitch motions of the floating platform cause temporal variations in hydrostatic pressure along the wetted surface. These fluctuations arise from changes in the submerged geometry and waterplane position and act as a primary source of restoring forces that counteract platform motion. The time-varying hydrostatic pressure was calculated using the relationship given in Eq. (7), which accounts for the instantaneous vertical displacement and the rotational angles of the platform. The resulting pressure field was then mapped onto the structural elements to represent the dynamic restoring behavior. Accurate reconstruction of this pressure component is essential for capturing the hydrostatic stiffness characteristics of the platform and ensuring that the structural analysis reflects realistic restoring forces under combined environmental loading. Here, ρ is the density of seawater. X3 is the vertical distance due to heave motion. θ1 and θ2 are the roll and pitch angles. The coordinate pair (x, y) indicates the positional distance from the rotation center to element i, respectively:
The roll and pitch rotations are defined about the platform center of gravity, which is taken as the rotation center. The coordinates represent the horizontal distances from this center to the centroid of element i, ensuring a clear physical interpretation of the hydrostatic pressure variation.
3.5 Wave Pressure
The wave pressure consists of the radiation pressure, which is proportional to the six degrees of freedom (6-DOF) motion of the floating body, and diffraction pressure, which is proportional to the incident wave elevation. The radiation pressure represents the hydrodynamic reaction because of platform motion, while the diffraction pressure reflects the pressure generated by the interaction between the incident waves and the floating structure.
In this study, the time-series platform motion and wave-elevation data were directly transformed into the frequency domain using a discrete Fourier transform (DFT). The frequency-domain data were then combined with the pressure transfer functions calculated from KR3D. The combined pressure components were then converted back into the time domain using an inverse Fourier transform (IFFT). The reconstructed wave pressures were mapped to the corresponding structural elements using the geometric information from the hydrodynamic panel model (Fig. 5). This process ensures phase consistency in the time domain and accurately reproduces the interaction between floating-body motion and local wave pressure.
Example of wave pressure
The radiation and diffraction pressures were reconstructed using impulse response functions (IRFs) derived from the KR3D frequency domain coefficients. The IRFs were truncated to a finite duration, and a high-frequency cutoff was applied to suppress numerical noise during the FFT/IFFT process. A mild smoothing filter was also introduced to ensure numerical stability.
4. Verification
The verification stage was carried out to confirm that the reconstructed load components accurately reflect the loading environment produced by global dynamic analysis and that they can be applied consistently within the structural model. The accuracy of each component and the combined load field resulting from their simultaneous application must be validated because the proposed methodology synthesizes aerodynamic, hydrodynamic, hydrostatic, and inertia-related loads. Ensuring this consistency is essential for reliable time domain structural evaluation.
The verification procedure consisted of four complementary assessments. In the first step, the reconstructed radiation and diffraction pressures were compared with the reference hydrodynamic pressures obtained from the KR3D frequency domain solver. This comparison assessed whether the frequency-to-time reconstruction preserves the correct amplitude and phase relationships associated with wave-induced loads. The second part of the verification focused on the fluctuating hydrostatic pressure. Here, the restoring forces derived from the reconstructed pressure field were compared with those calculated directly from platform motions, confirming that the hydrostatic stiffness characteristics of the platform had been accurately reproduced.
The third verification step examined the overall load equilibrium. All reconstructed load components were transformed into the body-fixed coordinate system and combined, and the resulting total force and moment vectors were compared with the inertia forces calculated from the global dynamic simulation. This step ensured that the reconstructed loads satisfy global equilibrium, which is essential for preventing numerical drift or artificial deformation patterns in the structural model. Finally, the structural responses resulting from the reconstructed loads were analyzed. The resulting deformation shapes and stress distributions were examined to confirm that the loads were applied smoothly to the finite element mesh and that they reproduce physically meaningful structural behavior without generating unrealistic numerical artifacts.
Through these verification steps, the accuracy, consistency, and physical adequacy of the reconstructed load components were comprehensively evaluated. The results confirmed that the proposed load-generation methodology produces load fields that can be used reliably for a detailed structural assessment, including ultimate and fatigue-limit state evaluations.
4.1 Wave Loads
The verification of the reconstructed wave loads focused on assessing whether the radiation and diffraction pressure components accurately reproduce the hydrodynamic behavior predicted by the KR3D solver. These components are essential for representing wave-induced forces acting on the floating platform, and their correct reconstruction is critical for reliable structural loading. The reconstructed pressures showed close consistency with the reference time series in terms of amplitude, temporal evolution, and phase, as shown in Figs. 6–9. In addition to a direct time-series comparison, the reconstructed pressures exhibited appropriate spectral characteristics when evaluated across the primary wave frequencies. The peak energy levels and the distribution of hydrodynamic responses across the frequency range matched well with the reference data, confirming that the reconstruction process captured the low-frequency and wave-frequency dynamics. Minor deviations observed in the low-frequency tails remained within acceptable bounds and did not affect the overall integrity of the applied loads. These verification results showed that the reconstructed radiation and diffraction pressures can be applied with confidence to the structural model for time-domain analysis.
Comparison of the radiation pressure (time history)
Comparison of the radiation pressure (spectrum)
Comparison of the diffraction pressure (time history)
Comparison of the diffraction pressure (spectrum)
The slightly increased residuals at the beginning and end of the time series were attributed to edge effects arising from the frequency-to-time transformation process. These effects arise from the finite length of the FFT/IFFT operations and the truncation of the frequency-domain signals, which may introduce minor spectral leakage and wrap-around artifacts near the signal boundaries. As a result, small deviations appeared when the reconstructed loads were compared with the reference inertia forces in these regions. On the other hand, the magnitude of the deviation remained within a few percent of the peak load amplitude and was negligible relative to the dominant hydrodynamic and inertia-induced loads. Moreover, these deviations were confined to the boundary regions of the time series and did not affect the steady-state portion used for structural response analysis. Only the steady-state segment of the reconstructed loads was applied in the finite element simulations to ensure robustness. Therefore, the observed deviations did not compromise the validity or the physical consistency of the proposed load-generation methodology.
4.2 Restoring Force
The time-varying hydrostatic pressure was used to determine if the restoring forces generated from the reconstructed hydrostatic field accurately reflect the heave, roll, and pitch responses of the platform. The hydrostatic restoring behavior is a key contributor to the overall stability and motion characteristics of floating structures, making it essential to confirm that this component is correctly reproduced. The reconstructed restoring force in heave and the restoring moment in pitch closely followed the reference signals derived from the global motion data, as shown in Figs. 10–13. The agreement in the magnitude and phase suggests that the formulation provided in Eq. (6) captures the influence of instantaneous displacement and rotation on the hydrostatic pressure distribution.
Comparison of the restoring force in the z-direction (time history)
Comparison of the restoring force in the z-direction (spectrum)
Comparison of the restoring moment in the y-axis (time history)
Comparison of the restoring moment in the y-axis (spectrum)
Furthermore, the reconstructed restoring components respond appropriately to variations in the motion amplitudes and wave excitation levels of the platform. This behavior confirms that the reconstruction method reliably reflects the changes in the submerged geometry and waterplane position, both of which govern the hydrostatic stiffness. Accurate representation of this behavior is essential to avoid numerical imbalances in the structural model and to ensure that subsequent stress calculations are physically meaningful. Overall, the verification confirms that the reconstructed hydrostatic forces provide a stable and realistic contribution to the time domain structural analysis.
4.3 Total Force
The total applied force was verified to confirm that the reconstructed load components collectively satisfy the global equilibrium conditions of the floating platform. At each time step, all reconstructed forces and moments, including tower base loads, mooring tensions, radiation and diffraction pressures, hydrostatic restoring forces, and inertia-related terms, were summed in the body fixed coordinate system. The resulting total load vector was then compared with the inertia forces extracted directly from the global dynamic simulation. The summed total force exhibited excellent agreement with the inertia forces throughout the simulation period, as shown in Figs. 14 and 15. These results confirm that the proposed load generation procedure preserves global equilibrium, which is essential for preventing artificial drift, unintended rigid-body motions, or unrealistic stress developments within the structural model.
Total load summation in the x-direction
Total load summation in the z-direction
4.4 Structural Response
The final step in the verification process involved evaluating the structural responses produced by the reconstructed loads. This assessment ensured that the loads were applied smoothly to the finite element model and that they generated deformation and stress patterns consistent with the expected behavior of the floating platform under combined environmental loading. The structural analysis examined the global deformation shapes and local stress distributions, providing a comprehensive indication of the physical realism of the applied loads.
The overall deformation patterns in the lower and upper regions of the platform followed the global motion characteristics observed in the dynamic analysis, as shown in Figs. 16 and 17. The structural model responds with smooth displacement fields, without exhibiting numerical artifacts such as localized stress spikes or irregular deformation gradients. In addition, the stress contours corresponded well with the regions of expected load concentration, confirming that the reconstructed pressure fields and external forces had been correctly transferred to the mesh. Hence, the load application method maintains continuity across structural components and accurately represents the dynamic interaction between the floating platform and its environment. Overall, the structural response results showed that the reconstructed loads satisfy the global equilibrium and produce physically consistent structural behavior, confirming the suitability of the proposed methodology for time-domain structural assessment.
Stress with a deform plot (bottom view)
Stress with a deform plot (Top view)
5. Conclusion
This paper presented an integrated time-domain load-generation methodology for a structural evaluation of semi-submersible floating offshore wind turbine (FOWT) platforms. The approach combines the hydrodynamic coefficients from KR3D with fully coupled aero-hydro-servo-elastic simulations performed in OpenFAST to reconstruct the key load components required for detailed structural analysis. The reconstructed loads included the tower base forces, mooring line tensions, radiation and diffraction pressures, fluctuating hydrostatic pressures, and inertia-induced internal pressures, all expressed in a form compatible with finite-element structural models.
The verification results showed that the proposed methodology accurately reproduces the loading environment predicted by the global dynamic simulation. The reconstructed wave-induced pressures exhibited strong agreement with hydrodynamic predictions in the amplitude and phase, confirming the fidelity of the frequency-to-time-domain transformation. The time-varying hydrostatic pressures, which govern heave, roll, and pitch restoring behavior, were also shown to match the restoring forces derived directly from platform motions, indicating that the method appropriately captures variations in submerged geometry and waterplane position. Furthermore, the combined load field satisfies global equilibrium with the inertia forces from the dynamic simulation, ensuring that the load components collectively maintain physical consistency. Structural response analyses confirmed that the applied loads generated smooth, realistic deformation shapes and stress distributions without numerical artifacts, further validating the reliability of the reconstructed loads.
Overall, the proposed framework provided a practical, physically consistent approach for linking global dynamic simulations with high-fidelity structural analysis. The method enabled accurate time-domain assessments of the structural performance and was suitable for the ultimate limit state (ULS) and fatigue limit state (FLS) evaluations of large-scale FOWT substructures. The methodology was modular and compatible with existing analysis tools. Therefore, it can be readily extended to different floating platform configurations, turbine capacities, and environmental conditions.
Notes
Beomil Kim serves on the journal publication committee of the Journal of Ocean Engineering and Technology and had no role in the decision to publish this article. No potential conflicts of interest relevant to this article are reported.
This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Climate, Energy & Environment (MCEE) of the Republic of Korea (NO. RS-2023-00238996 and RS-2024-00456423).
Nomenclature
F external
External force
M floater
Mass of a floater
Afloater
Acceleration of a floater
F wave
Force of a wave
M steel
Mass of steel
P i
Internal pressure applied to element i
xi, yi, zi
Center of element i
Fgravity
Gravity
F buoyancy
Force of buoyancy
F tower base
Force of the tower base
F mooring
Force of mooring
M ballast
Mass of ballast water
x0, y0, z0
Tank reference point