## 2 Coupled Analysis of Turbine and Support Structure
### Brief Introduction of Offshore Structural Analysis Software X-SEA  
The X-SEA finite element analysis software was developed for the analysis and design of floating and fixed offshore structures in oil/gas and wind farm platforms. The current version of X-SEA developed in Konkuk University, Seoul, Korea, is the result of extensive research and development of the finite element program FINAS [19], which was developed in Imperial College London. The solution of X-SEA ranges from simple static to highly advanced nonlinear dynamic analysis [20]. The hydrodynamics in X-SEA is based on the Morison equation and diffraction wave theory. The evaluation of fatigue life in the frequency domain can be carried out for oil/gas platforms under wind and wave motions. In addition, the evaluation of fatigue life in the time domain can be carried out for offshore wind turbine structures for various load combinations of turbine loads, wave loads, currents load etc. The safety of the offshore structures can be investigated using various design standard code checking using the API-RP-2A [21], Euro code 3, AISC, NORSOK and ISO19902. Offshore structural analysis options in X-SEA are listed in Table 1 and its element library is demonstrated in Table 2. The user-friendly graphical interface in X-SEA was developed using the pre/post processor software, GiD 14 [22]. The fixed offshore hydrodynamic analysis can be carried out to get the dynamic response in X-SEA. The X-SEA wave kinematics is based on the Airy wave theory, [PERSON]'s 5 th order, stream function, cnoidal and solitary wave theory [23]. The hydrodynamic force includes contributions from Morison's equation, added mass and damping contributions and incident wave excitation from linear diffraction. For a single member, the equation of motion within the limitations of the assumptions stated above is written as:  
\[\left(M+\widetilde{M}\right)\dot{U}+\left(C+\widetilde{C}\right)\dot{U}+KU= \frac{1}{2}C_{D}\rho A_{D}|u|u+C_{M}\rho V_{M}\frac{du}{dt} \tag{1}\]  
where \(\rho\) denotes water density, \(C_{D}\) and \(C_{M}\) denotes drag and inertia coefficients, \(u\) denotes the horizontal and vertical velocity of water particles and \(D\) is the diameter of the member. \(A_{D}\) denotes the projected area of the object perpendicular to the velocity and \(V_{M}\) is the volume of the displaced fluid. \begin{table}
\begin{tabular}{c c} \hline \multicolumn{1}{c}{**Solution Features of X-SEA**} \\ \hline Environmental load (wave, current, wind, marine growth, buoyancy, earthquake, self-weight etc.) \\ Regular (five kinds) and irregular wave (PM and JONSWAP Spectrum) \\
3D linear diffraction wave theory (shell and solid element) \\ Static analysis with load combinations \\ Frequency analysis \\ Three-dimensional prestressed concrete analysis using 3D solid and shell element \\ Geometrical and material nonlinear analysis of frame, shell and solid elements \\ Nonlinear time history dynamics (dynamics of large deformation of elastoplastic analysis using frame, shell \\ and solid elements) \\ Pile-soil-interaction foundation analysis (P-Y, T-Z and Q-Z) \\ Dynamic analysis in time domain and frequency domain \\ COG (center of gravity) \\ Automatic calculation of Stress Concentration Factor (SCF) with local joint flexibility \\ Fatigue damage analysis in time and frequency domain \\ Mooring analysis with seabed contact for floating offshore structures \\ Multiple calculation of FAST v8 wind turbine loads \\ Coupled analysis of FAST v8 and offshore structural analysis \\ Code checking (AISC, API, Euro Code 3, Norsok, DNV and IEC wind) \\ \hline \end{tabular}
\end{table} 
Table 1: Offshore structural analysis options of X-SEA.