# Numerical Analysis of Filament Wound Cylindrical Composite Pressure Vessels Accounting for Variable Dome Contour

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Dome Design

#### 2.1. Geodesic Paths

#### 2.2. Non-Geodesic Paths

#### 2.3. Dome Profile Equation

## 3. Dome-Cylinder Interface

## 4. Finite Element Model

^{®}was used for the analysis. The modelling of the composite overlap was aided by the wound composite modeller tool.

## 5. Results

#### 5.1. Liner Analysis

^{®}. With Nlgeom, ABAQUS

^{®}includes terms called as load-stiffeners, caused due to the application of load [24]. In addition, the membrane stiffness in response to transverse loading is considered by including geometric nonlinearity.

#### 5.2. Composite and Liner Analysis

## 6. Conclusions

^{®}. Due to the activation of the load-stiffeners, the stress in the cylindrical section was higher and the stress peaks at the dome-cylinder interface were not observed when compared to the analysis without activation of nonlinear geometry. Secondly, the same liner model was overwrapped with one layer of carbon-epoxy composite with the same winding angle for all the cases. There was negligible secondary stress observed in the dome section, which is in agreement with the analytical results. Considerable secondary stresses are observed at the dome-cylinder interface in all the cases. There was an increasing trend in the secondary stress with a reduction of the slope at the vicinity of the interface. This secondary stress is caused due to the bending and out of plane shear stress, the former is due to the change in the radius of curvature and the latter is expected to be caused by a thickness change and observed to reach a maximum at a distance from the dome-cylinder joint and not exactly at the joint itself. Lastly, the shear stress distribution in a real pressure vessel with its dome designed using netting theory and its failure mechanism is presented. To this end, the important understanding is that the secondary stress has an impact mainly at the dome-cylinder interface, especially critical for thick walled cylindrical composite pressure vessels which are manufactured for high pressure storage and crucial to be considered during the design phase. While this could also be present at the boss-dome junction, this requires a much more complex analysis. These numerical results require more complex experimental validation with suitable strain measurement techniques.

## Author Contributions

## Funding

## Acknowledgments

^{®}. J. Sackmann acknowledges the How2MultiWind research project funding from the Federal Ministry for Economic Affairs and Energy (BMWi).

## Conflicts of Interest

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**Figure 15.**Sectional view of a dome-cylinder interface showing the thickness jump due to the hoop and polar winding.

**Figure 16.**Failure mechanism of the pressure vessel. Failure pressure of 113.4 MPa. One of the reasons for the failure could be the secondary stress at the dome-cylinder interface. The influence of the metallic boss present in this case is not considered; however, it cannot be neglected.

Carbon-Epoxy UD—Orthotropic | |||||||
---|---|---|---|---|---|---|---|

[MPa] | [MPa] | [-] | [-] | [MPa] | [MPa] | ||

${E}_{\parallel}=125588$ | ${E}_{\perp}=7700$ | ${\nu}_{\perp \Vert}=0.3$ | ${\nu}_{\perp}=0.21$ | ${G}_{\perp \Vert}=5600$ | ${G}_{\perp}=3700$ | ||

Carbon Epoxy UD—Orthotropic—Strength | |||||||

[MPa] | [MPa] | [MPa] | [MPa] | [MPa] | [MPa] | ||

${\sigma}_{\parallel}^{+}=1819$ | ${\sigma}_{\perp}^{+}=72$ | ${\sigma}_{\parallel}^{-}=1150$ | ${\sigma}_{\perp}^{-}=152$ | ${\tau}_{\perp \Vert}=90$ | ${\tau}_{\perp}=70$ | ||

Liner (LDPE)—Isotropic | |||||||

[MPa] | [-] | ||||||

$E=171.4$ | $\nu =0.42$ | ||||||

Liner (HDPE)—Isotropic | |||||||

[MPa] | [-] | ||||||

$E=1500$ | $\nu =0.42$ |

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**MDPI and ACS Style**

Jois, K.C.; Welsh, M.; Gries, T.; Sackmann, J.
Numerical Analysis of Filament Wound Cylindrical Composite Pressure Vessels Accounting for Variable Dome Contour. *J. Compos. Sci.* **2021**, *5*, 56.
https://doi.org/10.3390/jcs5020056

**AMA Style**

Jois KC, Welsh M, Gries T, Sackmann J.
Numerical Analysis of Filament Wound Cylindrical Composite Pressure Vessels Accounting for Variable Dome Contour. *Journal of Composites Science*. 2021; 5(2):56.
https://doi.org/10.3390/jcs5020056

**Chicago/Turabian Style**

Jois, Kumar C., Marcus Welsh, Thomas Gries, and Johannes Sackmann.
2021. "Numerical Analysis of Filament Wound Cylindrical Composite Pressure Vessels Accounting for Variable Dome Contour" *Journal of Composites Science* 5, no. 2: 56.
https://doi.org/10.3390/jcs5020056