## 5 Cylinder Tube Stacking Sequence Definition
### The Radial Deformation Analysis  
The composite cylinder tube allows a greater radial expansion than its steel counterpart, especially when the wall thickness is kept minimal and UHM fiber is not used; this compliance reduces the effectiveness of the piston-bearing bands and sealing. However, the event of the pressure asymmetry needs to be considered since only one chamber is pressurized at a time.  
Simplified linear FE analyses show an \(S\)-shaped wall deformation centered at the sealing point, with small overshoots due to the plate bending stiffness.  
The reference steel geometry and the multi-material cylinder named Case B as shown in Table 6 were investigated. The modeling of the composite cylinder was obtained by superposition on the structural requirements previously discussed. This solution consists of (a) a metallic liner (\(t_{\text{liner}}\) = 2 mm) and (b) UHM composites plies (\(t_{90^{\circ}}\) = 5.3 mm and \(t_{0^{\circ}}\) = 2.0 mm). The cylinder tube stacking sequence was modeled by homogeneously distributed regions along its thickness; the circumferential plies are alternated by the axial plies, and the stacking sequence is as follows [liner, 0,90,0,90,0,90,0,90,0] moving from the inner cylinder radius to the outer radius.  
The elements adopted to discretize the barrel are four-noded, quadrilateral, isoparametric elements for axisymmetric applications (element type = 10, see [37]) with 15 elements along the wall thickness with an average size equal to 1 mm. The material properties of the reference cylinder and of the composite counterpart are reported in Tables 1 and 4.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **t\({}_{\text{\tiny\text{\tiny\text{\tiny\text{\tiny\text{\tiny\text{\tiny\text{ \tiny\text{\tiny\text{\tiny\text{\tiny\text{\tiny\text{\tiny\text{\tiny\text{ \text{ \text{ \texttexttext{ \texttexttexttexttext {    \texttexttexttexttext{ }}}}}}}}}}}}}}\) & \\ \hline A & 2.0 & 5.3 & 0.0 & no liner \\ B & 2.0 & 5.3 & 0.0 & 2.0 \\ C & 2.0 & 5.3 & 2.0 & 2.0 \\ D & 2.0 & 5.3 & 4.0 & 2.0 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The thickness of plies and of the inner liner subdivided by orientation angle \(\phi\), adopted for the test cases studied for the composite cylinder tube.  
Both the reference and the multi-material cylinder were loaded at the inner radius for a half of their axial extent by the burst pressure \(p_{\text{i}}\) equal to 67 MPa.  
Figure 5 shows the radial deformation of the cylinder collected at the inner radius of the cylinder (\(u_{\text{r}|\text{r}=\text{r}_{\text{i}},\text{s}}\)), normalized with respect to the radial deformation evaluated far from the loaded-unloaded transition cross-section at the inner radius of the cylinder (\(u_{\text{r}|\text{r}=\text{r}_{\text{i}},\text{s}=\text{f}}\)) along the cylinder axial extent (s). The parameter \(s\) is null at the mid-span axial length of the cylinder; the pressurized chamber appears on the right-hand side of Figure 5.  
The normalized radial deformation decreases asymptotically to zero moving within the unloaded portion and increases to the value returned by the Lame's solution moving within the loaded portion. It is clear that the sealing acts on a cylinder section where radial deformation is half its asymptotic value. The maximum value of the normalized radial deformation of both the reference and the multi-material cylinder are comparable.  
The radial inflation also decreases more rapidly in the composite Case B; the piston-bearing band on the unloaded side pairs an almost undeformed cylinder section.