**2.5 Variations of section "E"**

In an effort to improve the performance of the promising section "E", additional designs derived from section "E" were analyzed (**Figure 5**). Moreover, a design matrix (**Table 5**) was constructed based on defined design parameters: composite


**Table 5.** *Section E variations test matrix.*


**Table 6.** *Design optimization test matrix.*

**31**

usage.

**3. Results**

in 2.3.7 & 2.3.8.

*Sustainable and Efficient Hydroforming of Aerospace Composite Structures*

thickness, yoke plate material and corner radius. This allowed for a systematic testing procedure to evaluate the performance of the different configurations product

Section "A" was found to offer superior structural properties compared to the other designs analyzed in this project. This section allows for the smoothest stress distribution along the composite winding. However, as previously stated, the design exploration aims to find a cross section with a smaller height, such as section "E" (**Figure 5**). Given the poor performance of the custom designed sections (B–E, E1–E4) a new design exploration was carried out by defining the main geometry as an ellipse. By varying the major and minor axis dimensions, subsequently, a more systematic approach was adopted for the optimization of the cross section. Section "A" was used as the starting point, and from there, the design variables (**Figure 2b**) were parameterized. The test matrix for the ellipsoidal optimization of the cross section is presented in **Table 6**. Configuration 13 is the previously optimized circular section and is used as the baseline for this optimization. The objective is to reduce the overall height and material

As part of the optimization process intended to reduce the overall height and material usage of the pressure vessel's cross section, the press cylinder was removed from the design. A noticeable lack of stress near the yoke plates interface (**Figure 6a**) encouraged the addition of an angled cut (non-horizontal) interfaces between the yoke plates. The advantages of using a non-horizontal yoke plate contact interface are visible in the results for design configurations 2, 8, 9 (**Figure 6b, 9c**, & **9d**, respectively), as the stress near the contact of the yoke plates increases substantially but remains below the material yield point. A decrease in the press cylinder stress was also achieved, so the press cylinder thickness was gradually reduced (**Figur 6c**) until it was completely removed from the assembly. With the press cylinder removed, we concluded that the angled yoke plates' interfaces were not essential, since a simpler horizontal allowed for stress magnitudes within the required limits, as depicted in **Figure 6e** (configuration 13). This resulting cross section design obtained from the optimization process was set as the base for the subsequent optimization procedures, and the finite element model was modified to account for the removal of the press cylinder, as described

Sections "B," "C," "D," and "E" showed a considerably inferior performance to section "A." However, the surface area of their yoke plates and their overall height (with the clear exception of Section "B") was considerably less than that of section "A." The substandard performance of these sections can be directly associated with the change in curvature of the composite winding due to the change in the heightto-length ratio for the overall cross section. As this ratio increases (height < length),

the curvature radius decreases, and thus, stress concentrations appear in the

*DOI: http://dx.doi.org/10.5772/intechopen.81505*

of the multiple design parameter combinations.

**2.6 Section "A": ellipsoidal optimization**

**3.1 Section "A" optimization results**

**3.2 Section "B," "C," "D," and "E" FEA results**

thickness, yoke plate material and corner radius. This allowed for a systematic testing procedure to evaluate the performance of the different configurations product of the multiple design parameter combinations.
