**3.5 Optimization results**

A feasible design configuration (**Figure 10**) resulted from this design exploration (marked green in **Table 5**). At first view, it appears to be nearly circular,

although it is not. The section has a length-to-height ratio of 1.1045 while maintaining stress concentrations within the allowable limit. The optimized curvatures resulting from the specially selected design parameters provide a reduction of up to 23% (139 mm) on the total cross section height when compared to the original Section "A" design (including press cylinder) (602 mm), or 14% when compared to the optimized circular section "A" without the press cylinder. Similarly, the overall height of the yoke plates was reduced 25% with respect to the original section "A." One particular drawback of the proposed design is the necessary increase in composite winding thickness. A more detailed sensitivity analysis can help determine the optimal composite winding thickness between the bounds set forward by this work in order to adjust the maximum stress on both the composite winding and yoke plates to be equal to the predefined design stress (yield stress).

Note that the yoke plate surface area subjected to pressure is twice as large as that of the side yoke plates. Thus, a greater net force is exerted on the top and bottom yoke plates when compared to the side plates. The applied pressure load produces outward displacement or expansion of the whole structure. However, the composite winding tends to expand more in the vertical direction due to the greater surface area producing a higher total magnitude of force. The vertical displacement generates a contraction of the sides of the composite structure, which opposes the expansive behavior caused by the lateral pressure load. Consequently, the resultant lateral forces acting upon the sides yoke plates have a considerably smaller magnitude than that of the vertical force. This allows for the use of very side yoke plates, as shown in configuration 28. A non-horizontal angled cut is not practical for these design configurations due to the reduced width of the side yoke plates. Otherwise, it may well be possible to further reduce yoke plate height by means of a non-horizontal yoke plate contact interface.

Note that the increase in composite winding thickness may induce additional manufacturing costs, which must be studied in detail. The overall advantage of having a reduced cross section height must be of significant value to justify the increase in cost due to additional composite material. A through manufacturing analysis would be beneficial to determine whether the cost of increasing the composite material usage or increasing the overall yoke plate size yields the best possible outcome.

### **3.6 ANOVA: analysis of variance of design variables**

Finite element analysis results of each parameterized configuration proposed in the test matrix for Section "E" variations were statistically tested to estimate the

**37**

their steel counterparts.

sections E1–E4.

**Figure 11.**

**Figure 12.**

**4. Conclusions**

section types were investigated.

*Sustainable and Efficient Hydroforming of Aerospace Composite Structures*

*Effect of design parameter on composite winding stress and yoke plate stress respectively.*

effect of each design variable and their possible combined effects on the maximum stress. An analysis of variance (ANOVA) of the stress response at a specific point in the geometry of each design configuration exposes which design parameter has the greatest effect on the composite winding and yoke plate stresses of the model, respectively (shown in the form of Pareto charts in **Figure 11**). In most cases, plate height has the greatest effect on both stress and displacement responses, followed by the yoke plates material. Aluminum yoke plates show better performance than

*Accumulative effect of design parameter on composite winding stress and yoke plate stress.*

The accumulated effects in **Figure 11** are plotted in **Figure 12** to illustrate the principal and most sensitive response. It can be concluded that Yoke plate stress is the most sensitive response to changes in the design parameters for custom

In this study, a multi-physics approach was employed to derive the performance of a type of pressure vessel. Pressure loads were transferred asymmetrically through multiple materials and geometries. The mechanical properties and FEA of various

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

**Figure 10.** *Ellipsoidal optimization design configuration 28 stress results.*

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

#### **Figure 11.**

*Environmental Impact of Aviation and Sustainable Solutions*

yoke plate contact interface.

**3.6 ANOVA: analysis of variance of design variables**

*Ellipsoidal optimization design configuration 28 stress results.*

although it is not. The section has a length-to-height ratio of 1.1045 while maintaining stress concentrations within the allowable limit. The optimized curvatures resulting from the specially selected design parameters provide a reduction of up to 23% (139 mm) on the total cross section height when compared to the original Section "A" design (including press cylinder) (602 mm), or 14% when compared to the optimized circular section "A" without the press cylinder. Similarly, the overall height of the yoke plates was reduced 25% with respect to the original section "A." One particular drawback of the proposed design is the necessary increase in composite winding thickness. A more detailed sensitivity analysis can help determine the optimal composite winding thickness between the bounds set forward by this work in order to adjust the maximum stress on both the composite winding and

Note that the yoke plate surface area subjected to pressure is twice as large as that of the side yoke plates. Thus, a greater net force is exerted on the top and bottom yoke plates when compared to the side plates. The applied pressure load produces outward displacement or expansion of the whole structure. However, the composite winding tends to expand more in the vertical direction due to the greater surface area producing a higher total magnitude of force. The vertical displacement generates a contraction of the sides of the composite structure, which opposes the expansive behavior caused by the lateral pressure load. Consequently, the resultant lateral forces acting upon the sides yoke plates have a considerably smaller magnitude than that of the vertical force. This allows for the use of very side yoke plates, as shown in configuration 28. A non-horizontal angled cut is not practical for these design configurations due to the reduced width of the side yoke plates. Otherwise, it may well be possible to further reduce yoke plate height by means of a non-horizontal

Note that the increase in composite winding thickness may induce additional manufacturing costs, which must be studied in detail. The overall advantage of having a reduced cross section height must be of significant value to justify the increase in cost due to additional composite material. A through manufacturing analysis would be beneficial to determine whether the cost of increasing the composite material usage or increasing the overall yoke plate size yields the best possible outcome.

Finite element analysis results of each parameterized configuration proposed in the test matrix for Section "E" variations were statistically tested to estimate the

yoke plates to be equal to the predefined design stress (yield stress).

**36**

**Figure 10.**

*Effect of design parameter on composite winding stress and yoke plate stress respectively.*

#### **Figure 12.**

*Accumulative effect of design parameter on composite winding stress and yoke plate stress.*

effect of each design variable and their possible combined effects on the maximum stress. An analysis of variance (ANOVA) of the stress response at a specific point in the geometry of each design configuration exposes which design parameter has the greatest effect on the composite winding and yoke plate stresses of the model, respectively (shown in the form of Pareto charts in **Figure 11**). In most cases, plate height has the greatest effect on both stress and displacement responses, followed by the yoke plates material. Aluminum yoke plates show better performance than their steel counterparts.

The accumulated effects in **Figure 11** are plotted in **Figure 12** to illustrate the principal and most sensitive response. It can be concluded that Yoke plate stress is the most sensitive response to changes in the design parameters for custom sections E1–E4.

#### **4. Conclusions**

In this study, a multi-physics approach was employed to derive the performance of a type of pressure vessel. Pressure loads were transferred asymmetrically through multiple materials and geometries. The mechanical properties and FEA of various section types were investigated.

The results of the study demonstrate that pressure containment of 165.48 MPa (24,000 psi) is feasible using carbon fiber bobbin wound over a 7075-T6 yoke plate. The simulations show that asymmetric internal loading of a rectangular high-pressure zone containing working fluid does indeed create localized hot spots of pressure in both the containment windings and the associated yoke plates. The primary surprise is that bridge-like bending deflection in the yoke plates is one of the major concerns of the system. This bending deflection caused catastrophic containment winding failure to occur at the centerline of the outer containment windings. Yoke plate deformation would also ultimately cause forming chamber deflection and leakage.

The study reinforces the idea that a near-circular cross section provides the best overall stress distribution throughout the composite winding. However, this comes at the expense of increasing the overall size of the yoke plates. By modifying the design parameters, principally the yoke plates' height, and adjusting the composite winding to seamlessly wrap around the new configuration, a reduction in the yoke plate size is achieved while attaining stress concentrations below each material limit.

L/H ratio defines the overall curvature of the composite, and the closer it gets to 1, the better the performance. However, the stress in the composite is most of the time less than its strength. The main problem has to do with the yoke plates. Early study sections 20–23 have round cross sections, but the stresses induced into the yoke plates exceed the yoke plate's material yield point, thus must be discarded.

Analysis of variance (ANOVA) of the stress responses at a specific point in the geometry reveal that yoke plate section height, yoke plate material, and the overall cross-section curvature radius (length-to-height ratio) are the driving design parameters to achieve a successful and improved solution.

One of the key findings of relevance is the use of an angled wedge integral to the upper yoke plate to create a positive pressure transfer shear plane with the side yoke plates. This positive surface-to-surface contact area allows for lateral expansion compression pressure loads be transferred into the upper yoke plate as surface tension. This additional tension induced into the upper plate helps to stabilize the "bridge bending" tendency of the upper and lower yoke plates. It also reduces the loads transferred by the side yoke plates into the outer fiber windings by confining lateral yoke plate movement expansion.

After testing greatly varied profiles and cross sections, we conclude that a near-round ellipse section successfully accommodates a pressure of 165.48 MPa (24,000 psi). This is using mildly interfacing yoke plates to balance the structure. This solution is conceptually similar to a traditional legacy design section configuration. However, this conclusion is a point of reference - not a final design. It should be considered a proof-of-concept validation point that illustrates that a cross section can be developed to meet the functional performance criteria required using carbon fiber and aluminum in place of steel. As a result, the section as it stands offers a significant reduction in weight over the traditional "steel over steel" fabrication method. A thin-wall section, light weight, reduction or elimination of press cylinder wall achieves a 65% overall weight reduction in similar design due to a shift from steel wound with high tensile steel tape to aluminum wound with carbon fiber.
