**3.3 Section "E" variants FEA results**

*Environmental Impact of Aviation and Sustainable Solutions*

composite winding. However, a small length-to-height ratio (height > > length) similar to Section "B" is also undesired, as the stress in the side plates increases

*Stress results for ellipsoidal section design configurations: (a) configuration 1, (b) configuration 2,* 

*(c) configuration 8, (d) configuration 9, (e) configuration 13.*

As is the case with section "A" results, a noticeable lack of stress near the yoke plates interface is observed in the results for sections "B," "C," and "D". Likewise, the stress magnitude on the side yoke plates is less than that of the main yoke plates. A non-horizontal angled cut contact interface could have been implemented for

**32**

considerably.

**Figure 6.**

The section E variants appeared to be the ideal candidates for an optimized designed. This was not the case, as the E section proved not to be strong enough to withstand the applied pressure load. The failure mechanism was primarily located in the composite winding, at the inner surface of the corner rounds. To reduce the stress at this location, the corner radii must be increased, although to achieve this, the height of the yoke plates must be increased, which represents a step back

**Figure 7.** *Stress results for: (a) section "B," (b) section "C," (c) section "D," (d) section "E".*

toward the original circular cross section design. We concluded that cross sections that tightly wrap around the inner slot where the pressure is applied are most likely to stress beyond the permissible limit, primarily due to high stress concentration around the sharp radii near the corners. Due to the failure of all the design configurations proposed in the test matrix for Section "E" variations (**Table 5**), only the stress results for the baseline configurations for each custom Section E1–E4 are provided in **Figure 8** to illustrate the stress concentration areas in the different cross section designs.

As stated before, none of the custom design sections (B–E & E1–E4) resulted in feasible designs. Returning to the last feasible configuration (Section "A," design configuration 13), a new design exploration was carried out by defining the main geometry as an ellipse. By varying the major and minor axis dimensions, an ellipsoidal shape with a smaller height was achieved. The design intent and evolution are shown in **Figure 9**, where stress results for key design iteration are provided. The minor axis is reduced considerably during the first configurations, increasing the length-to-height ratio and consequently the stress responses. The minor axis had to be increased back again until the design stress limits were met. Different non-horizontal angled cut contact interfaces were also tested, such as, 45° and −35° interface angles. Based on results and the original idea behind the concept, we concluded that the non-horizontal contact interface must have a negative angle (on the right side of the vertical symmetry plane) with respect to the horizontal plane to be beneficial for the design (achieve load transfer from yoke plate to side yoke plate). The stress results demonstrate that the length-to-height ratio is an important design parameter, which must be close to 1 to achieve good stress distributions along the composite winding. Regardless of the final configuration length-to-height ratio being close to one, i.e., the cross section being almost circular, a considerable reduction in cross section height was achieved.

#### **Figure 8.**

*Stress results for section "E" variations design configurations: (a) section E1, (b) section E2, (c) section E3, (d) section E4.*

**35**

**Figure 9.**

**3.5 Optimization results**

*Sustainable and Efficient Hydroforming of Aerospace Composite Structures*

**3.4 Ellipsoidal optimization of circular section "A" FEA results**

A feasible design configuration (**Figure 10**) resulted from this design explora-

tion (marked green in **Table 5**). At first view, it appears to be nearly circular,

*Stress results for the design configurations produced during the ellipsoidal optimization procedures. (a) Configuration 15, (b) configuration 17, (c) configuration 18, (d) configuration 20, (e) configuration 28.*

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

### *Sustainable and Efficient Hydroforming of Aerospace Composite Structures DOI: http://dx.doi.org/10.5772/intechopen.81505*

#### **Figure 9.**

*Environmental Impact of Aviation and Sustainable Solutions*

section designs.

was achieved.

toward the original circular cross section design. We concluded that cross sections that tightly wrap around the inner slot where the pressure is applied are most likely to stress beyond the permissible limit, primarily due to high stress concentration around the sharp radii near the corners. Due to the failure of all the design configurations proposed in the test matrix for Section "E" variations (**Table 5**), only the stress results for the baseline configurations for each custom Section E1–E4 are provided in **Figure 8** to illustrate the stress concentration areas in the different cross

As stated before, none of the custom design sections (B–E & E1–E4) resulted

in feasible designs. Returning to the last feasible configuration (Section "A," design configuration 13), a new design exploration was carried out by defining the main geometry as an ellipse. By varying the major and minor axis dimensions, an ellipsoidal shape with a smaller height was achieved. The design intent and evolution are shown in **Figure 9**, where stress results for key design iteration are provided. The minor axis is reduced considerably during the first configurations, increasing the length-to-height ratio and consequently the stress responses. The minor axis had to be increased back again until the design stress limits were met. Different non-horizontal angled cut contact interfaces were also tested, such as, 45° and −35° interface angles. Based on results and the original idea behind the concept, we concluded that the non-horizontal contact interface must have a negative angle (on the right side of the vertical symmetry plane) with respect to the horizontal plane to be beneficial for the design (achieve load transfer from yoke plate to side yoke plate). The stress results demonstrate that the length-to-height ratio is an important design parameter, which must be close to 1 to achieve good stress distributions along the composite winding. Regardless of the final configuration length-to-height ratio being close to one, i.e., the cross section being almost circular, a considerable reduction in cross section height

*Stress results for section "E" variations design configurations: (a) section E1, (b) section E2, (c) section E3,* 

**34**

**Figure 8.**

*(d) section E4.*

*Stress results for the design configurations produced during the ellipsoidal optimization procedures. (a) Configuration 15, (b) configuration 17, (c) configuration 18, (d) configuration 20, (e) configuration 28.*
