## 2 Materials and Methods
### FE Modelling and Study Cases  
ANSYS Workbench 17.1 was utilized for the comparative study of vortex-induced vibration (VIV) for the FRP composite risers and steel riser with length to diameter ratio of 100. Initially, the natural frequencies of all the risers were analyzed using pre-stress modal analysis. For FRP composite risers, ACP (Pre), Static Structural and Modal modules were involved while for steel risers, only Static Structural and Modal modules were required. In order to achieve the VIV simulation in ANSYS Workbench 17.1, the following modules were included: Geometry, ACP (Pre), Transient Structural, Fluid Flow, ACP (Post) and System Coupling [19]. Generally speaking, Geometry was utilized to create the geometries of risers and flow zones; ACP (Pre) and ACP (post) were employed to include the data of materials and lamination information for composite risers (risers 2 and 3) and to show the stress and deformation response of every composite laminae, respectively; Transient Structural was used to simulate the dynamic responses of risers; System Coupling was applied to achieve the data transfer between Transient Structural and Fluid Flow. As mentioned in Section 2.2, the geometries of composite risers 2 and 3 were obtained from the design results of [PERSON] [20; 21; 27] and the finite element modelling method had been verified by [PERSON] [14] and [PERSON] [26]. The difference here was the load conditions which was current flow with different velocities. In this study, layered-structure method (LSM) [19] was employed for FRP composite riser simulation and their geometries are listed in Table 4. For the FRP composite risers, the data of material properties, the thicknesses of liner and composite laminate, reinforced fiber angles, the layer numbers of each lamina with different fiber orientations and the laminate stacking sequences were inputted in the module of ACP (Pre) and the stress and deformation response of every composite laminae \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Riser**} & **L.D.** & **O.D.** & **Length** & **t\_liner** & **t\_0** & **t\_\(\pm\)0** & **t\_90** & **\(\pm\)0** \\  & **(m)** & **(m)** & **(m)** & **Lay-ups** & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **(****)** \\ \hline
1 & 0.25 & 0.3 & 25 & X80 steel & & & & & \\
2 & 0.25 & 0.329 & 25 & [liner/90/(0/90)\({}_{10}\)] & 2 & 1.385 & & 2.15 & \\
3 & 0.25 & 0.311 & 25 & [liner/0\({}_{3}\)/(+53, -53)\({}_{5}\)/90\({}_{4}\)] & 2 & 1.70 & 1.64 & 1.75 & 53 \\ \hline \hline \end{tabular} Subscript numbers in Lay-ups represent the numbers of lamina with different fiber reinforcement angle.  
\end{table} 
Table 4: Geometries of risers. Figure 3: Cross-section for (**a**) steel riser joint and (**b**) composite riser joint. were obtained in ACP (Post). The possible bond-slip effect is a significant phenomenon of FRP layers, and this can be checked indirectly in post-processing stage by comparing the maximum interface forces and stresses with the reference pull-out resistances [48]. However, in this paper, the numerical model of the composite riser using LSM assumed a rigid connection between the components, i.e., perfect bonding was assumed and no bond-slip effect was considered to simplify the modelling. Then, the geometry and material data of FRP composite riser in ACP (Pre) were transferred to the Transient Structural module. Transient Structural was utilized to simulate the dynamic response of risers. In this module, the gravity, top-tension force, buoyancy, end support condition (simple support at the top end, fixed support at the bottom end) and the fluid solid interface were employed. After the whole simulation, the displacement history, global stress distribution etc., could be obtained. Fluid Flow (Fluent) was used to simulate the flow conditions. 10D (Y-direction) \(\times\) 20D (X-direction) \(\times\) 25 m (Z-direction) was set as the flow dimension, where D was the outside diameter of the risers.