## 4 Conclusions  
This paper presents a comparative VIV study of FRP composite risers (AS4-epoxy with titanium liner) with two geometries ([liner/90/(0/90)\({}_{10}\)] and [liner/0\({}_{3}\)/(+53, \(-53\))\({}_{5}\)/90\({}_{4}\)]) using a steel riser as the benchmark. The CFD simulation with coupled fluid-structure interaction was employed for nine different study cases considering a combination of different risers, tension forces, buoyancies, gravities and current conditions to investigate each riser's VIV characteristics including their natural  
Figure 15: Factor of safety of composite layers for 2.13 m/s in (**a**) riser 2-fiber direction, (**b**) riser 2-transverse direction, (**c**) riser 3-fiber direction, (**d**) riser 3-transverse direction and (**e**) riser 3-shear direction.  
frequencies, global displacements, global stresses and the stress distributions in every layer of the FRP composite risers. The results showed that:  
(1) VIV responses of displacements for all three risers at 2.13 m/s were about 30 times of those at 0.36 m/s and 3 times of those at 1.22 m/s; VIV responses of global stresses for all three risers at 2.13 m/s were about 10 times of those at 0.36 m/s and 3 times of those at 1.22 m/s; and only in the 100 year loop current condition (2.13 m/s), \"lock-in\" might occur for steel riser (riser 1) and optimized FRP composite riser (riser 3).  
(2) Displacements in in-line flow direction maintained at a relatively stable value and vibrated slightly after the initial growth, while the vibration in cross flow direction was obvious. In terms of the total displacement, that of the optimized FRP composite riser was the largest and that of steel riser was the smallest, i.e., the maximum total displacement for riser 3 was about three times of that for riser 1 and two times of that for riser 2 at all flow velocities.  
(3) End support conditions affected the displacement significantly, i.e., simple support lead to larger displacement compared to the fixed support.  
(4) Maximum von Mises stresses occurred at the top/bottom end of all risers, followed by the middle parts (above the middle point) of the risers, while at about \(-\)19 m, the minimum von Mises stresses happened. When the maximum von Mises stresses occurred at the top end, the top tension force played a key role, and when the maximum von Mises stresses occurred at the bottom end, the bending force was the most significant one. For the middle part, both tension and bending forces were essential.  
(5) The conventional FRP composite riser (riser 2) had the largest FS (168, 43.7 and 16.1 for 0.36 m/s, 1.22 m/s and 2.13 m/s, respectively) while the optimized FRP composite riser (73.7, 24.2 and 12.9 for 0.36 m/s, 1.22 m/s and 2.13 m/s, respectively) and steel riser (82.4, 31.6 and 12.1 for 0.36 m/s, 1.22 m/s and 2.13 m/s, respectively) had the similar FS, indicating the optimized composite riser could take advantage of the fiber strength more efficiently.  
Conceptualization, C.W.; methodology, C.W. and S.G.; validation, C.W. and S.G.; formal analysis, S.G.; investigation, M.S.; data curation, S.G.; writing--original draft preparation, C.W. and S.G.; writing--review and editing, C.W.; supervision, C.W. and B.H.; project administration, C.W. and Z.J.; funding acquisition, C.W.  
This research was funded by the Shandong Provincial Natural Science Foundation (ZR2017 LEE031), National Natural Science Foundation of China (51806130) and the Science and Technology Development Project of Zibo (2017 KJ040017).  
The authors declare no conflict of interest.