# FPSO Hull Structures with Sandwich Plate System in Cargo Tanks
## 6 Ultimate Strength Analysis
### Finite Element Model
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Structure** & **Plate Number** & **Equivalent Thickness [mm]** & **Structure** & **Plate Number** & **Equivalent Thickness [mm]** \\ \hline \multirow{4}{*}{Bottom} & Keel & 47 & & 22 S & 33 \\  & Cargo Area & 52 & Side Longitudinal & 23 S & 33 \\  & Ballast Tank & 44 & Bulkhead & 24 S & 42 \\ \hline \multirow{4}{*}{Side} & 5 & 46 & & 25 S & 47 \\  & 6 & 38 & & 5 H & 33 \\  & 7 & 35 & & 6 H & 25 \\  & 8 & 33 & & 7 H & 25 \\  & 9 & 33 & & 8 H & 26 \\  & 10 & 34 & & 9 H & 26 \\  & 11 & 34 & & 10 H & 26 \\  & 12 & 34 & & 17 T & 31 \\  & 13 & 34 & & 18 T & 30 \\ \hline \multirow{4}{*}{Deck} & 15 & 44 & & 19 T & 30 \\  & 16 & 46 & Transversal & 20 T & 28 \\  & 17 & 36 & Bulkhead & 21 T & 28 \\  & 18 & 34 & & 22 T & 28 \\  & 19 & 32 & & 23 T & 28 \\  & 20 & 32 & & 24 T & 28 \\  & 21 & 32 & & 25 T & 28 \\  & 22 & 33 & Web Frame Bottom & 1 & 29 \\ \cline{3-6}  & 23 & 33 & & 2 & 27 \\  & 24 & 37 & & 3 & 25 \\  & 25 & 46 & & 4 & 24 \\ \hline \multirow{4}{*}{Side Longitudinal} & 17 S & 40 & Web Frame Side & 5 & 23 \\  & 18 S & 36 & & 6 & 23 \\ \cline{1-1}  & 19 S & 33 & & 7 & 23 \\ \cline{1-1}  & 20 S & 32 & & 8 & 23 \\ \cline{1-1}  & 21 S & 32 & Web Frame Deck & 9 & 23 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Equivalent thickness for the steel plates. accurate solution can be obtained by using the single layer of shell elements for the same reasons as the equivalent thickness model described above. Although the use of solid elements can model the geometry to the degree of detail wanted, this implies a large number of nodes and elements, meaning large computational efforts. Therefore, the equivalent steel plate would have equal inertia to the plates obtained in Figure 5. Since the geometry should be the same, only the thickness was varied to obtain the equivalent plate. The new plates are shown in Table 8.  
For each type of element, there are several options to choose and the appropriate one depends on the type of the analysis pursuit. For the steel plates, the best type of element is the shell one. Furthermore, the most suitable for the scope of this study is SHELL181. In addition, a sensitivity analysis was performed in order to check how the results vary with the mesh size (Table 9). It compared the FPI with a refined one that has all elements with a size of 0.85 m. There were five main variables studied: neutral axis height from the baseline, the normal stress from the bottom and deck plates, the spring reaction at the ends and the time required to run the simulation for the static and ultimate load case. The first three parameters of the reference column were obtained through the beam theory using the geometric properties and loads, the spring reference is detailed, and the time static/ultimate was considered as a reference to the mesh proposed by the FPI rules. As it is expected, the refined mesh provided more accurate results compared to the FPI mesh. However, the computational time required to perform it was 72% and 116% more for the static and ultimate load cases, respectively. Moreover, the results obtained are similar to the reference ones. Thus, the best trade-off between the accuracy of results and computational time required is the one from the FPI rules, and this is the one used for all models. Uniaxial springs are used at the ends of the model as the boundary condition. According to the ANSYS Manual [20], one suitable element is the COMBIN14, which is a uniaxial spring-damper. Since it becomes a spring only, the user must input zero as the damping coefficient. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Structure** & **Plate** & **Thickness [mm]** \\ \hline \multirow{3}{*}{Bottom} & Keel & 72 \\  & Cargo & 72 \\  & Ballast & 72 \\ \hline \multirow{6}{*}{Longitudinal Bulkhead} & 17 & 33 \\  & 18 & 33 \\  & 19 & 31 \\  & 20 & 29 \\  & 21 & 27 \\  & 22 & 27 \\  & 23 & 27 \\  & 24 & 29 \\  & 25 & 35 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Equivalent thickness for the SPS panels.