# Composite Overwrapped Pressure Vessel Design Optimization Using Numerical Method

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Analytical Study of the Composite Overwrapped Pressure Vessel

_{0}is the radius of the polar axis, and R

_{tl}is the radius at the dome–cylinder tangent line. The exponent n controls the variation from the tangent line to the turnaround point [28].

- ${\alpha}_{cyl}=\mathrm{winding}\text{}\mathrm{angle}\text{}\mathrm{at}\text{}\mathrm{cylinder}\text{}\mathrm{or}\text{}\mathrm{dome}\text{}\mathrm{junction}$;
- ${t}_{cyl}=\text{}\mathrm{thickness}\text{}\mathrm{of}\text{}\mathrm{composite}\text{}\mathrm{at}\text{}\mathrm{cylinder}\text{}\mathrm{dome}\text{}\mathrm{juncture}$;
- ${x}_{cyl}=\mathrm{radius}\text{}\mathrm{at}\text{}\mathrm{cylinder}\text{}\mathrm{dome}\text{}\mathrm{juncture}$.

_{B}is the burst pressure of the liner in MPa, ${\sigma}_{u}$ is the ultimate strength of the material in MPa, T is the thickness of pressure vessel in mm, and D is the inner diameter of pressure vessel in mm.

_{cr}can be found by considering the thickness of the shell (t), diameter of the cylindrical shell (d), length (spacing) between the stiffeners (l), Young’s Modulus (E), and Poisson’s ratio (ν) as follows:

_{i}subjected to internal pressures (P

_{i}), which is given by:

_{1}, F

_{2}, F

_{11}, F

_{22}, F

_{12}, and F

_{66}are determined based on the used materials strength parameters as formulated in Equation (15).

#### 2.2. Finite Element Modeling of Composite Pressure Vessel

## 3. Results and Discussion

#### 3.1. Burst Pressure Analysis

#### 3.2. Effect of Stacking Sequence of Layers

#### 3.3. Fiber Angle Orientation Effect on Burst Pressure

#### 3.4. Fiber Stress–Strain Distribution in the COPV

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Type-I Pressure vessel production method, (

**b**) Filament winding layout for COPV production (reproduced from [12], an open access article distributed under the terms of the Creative Commons CC-BY license, which permits unrestricted use, distribution, and reproduction), and (

**c**) Geometrical overview of vessels type II-IV (Reproduced with permission from [13]; copyright © 2017 Elsevier Ltd., Amsterdam, The Netherlands).

**Figure 2.**COPV: (

**a**) fiber geodesic path on dome, (

**b**) schematic view of vessel coordinates, and (

**c**) fiber path on cylinder.

**Figure 4.**COPV: (

**a**) Dimensions’ layout, (

**b**) 3D model of the linear, and (

**c**) Stack sequence of lamina.

**Figure 9.**Maximum stress failure index: (

**a**) lower than 1 at load step 0.83 and (

**b**) greater than 1 at load step 0.835.

**Figure 10.**Tsai–Hill failure index (TSAIH): (

**a**) lower than 1 at load step 0.695 and (

**b**) greater than 1 at load step 0.7.

**Figure 11.**Tsai–Wu failure index: (

**a**) lower than 1 at load step 0.72 and (

**b**) greater than 1 at load step 0.725.

**Figure 12.**Hashin fiber compression failure index (HSNFCCRT): (

**a**) lower than 1 at load step 0.735, and (

**b**) greater than 1 at load step 0.74.

**Figure 13.**Hashin fiber tension failure index (HSNFTCRT): (

**a**) lower than 1 at load step 0.755, and (

**b**) greater than 1 at load step 0.76.

Property | Units | Value | |
---|---|---|---|

Aluminum (AL6061) | Density | (kg/m^{3}) | 1570 |

Young’s modulus | GPa | 74.12 | |

Poisson’s ratio (ν) | - | 0.3 | |

Ultimate shear strength | GPa | 0.6 | |

Elastic | Young’s modulus in direction 1 (E1) | GPa | 176.8 |

Young’s modulus in direction 2 (E2) | GPa | 10.3 | |

Poisson’s ratio in direction 12 (ν12) | - | 0.23 | |

Shear modulus in direction 12 (G12) | MPa | 4.8 | |

Hashin’s parameters | Tensile strength in direction 1(X^{T}) | GPa | 3.3 |

Compressive strength in direction 1 (X^{C}) | GPa | 1.7 | |

Tensile strength in direction 2 (Y^{T}) | GPa | 0.096 | |

Compressive strength in direction 2 (Y^{C}) | GPa | 0.289 | |

Shear strength in direction 1 (S^{L}) | GPa | 0.096 | |

Shear strength in direction 2 (S^{T}) | MPa | 0.096 | |

Damage Evolution | Longitudinal Tensile Fracture Energy (G^{lt}) | MJ/mm^{2} | 984.778 |

Longitudinal Compressive Fracture Energy (G^{lc}) | MJ/mm^{2} | 277.9966 | |

Transverse Tensile Fracture Energy (G^{tt}) | MJ/mm^{2} | 7.02575 | |

Transverse Compressive Fracture Energy (G^{tc}) | MJ/mm^{2} | 117.694 |

Case No. | No. of Layers | Winding Angle [°]/Ply Sequence | Calculated Burst Pressure Range (MPa) | Predicted Average Burst Pressure (MPa) |
---|---|---|---|---|

1 | 13 | PP* [15, −15] s | - | - |

2 | 13 | PP [30, −30] s | - | - |

3 | 13 | PP [45, −45] s | 19.7–20.5 | 20.1 |

4 | 13 | PP [55, −55] s | 20.7–27.756 | 24.228 |

5 | 13 | PP [60, −60] s | 17.7–24.75 | 21.225 |

6 | 13 | HH** [75, −75] s | 13.95–29.772 | 21.861 |

7 | 13 | HH [89, −89] s | 13.35–15.9 | 14.175 |

8 | 13 | PHP [25/−25/87.5/−25/87.5/−25/87.5] s | - | - |

9 | 5 | PP [55, −55] s | 20.115–28.515 | 24.315 |

10 | 8 | PP [55, −55] s | 21–27.99 | 24.495 |

11 | 14 | PP [55, −55] s | 20.7–27.9 | 24.3 |

12 | 20 | PP [55, −55] s | 20.859–27.759 | 24.309 |

13 | 21 | PP [55, −55] s | 20.706–27.756 | 24.231 |

14 | 27 | PP [55, −55] s | 20.8566–27.756 | 24.3063 |

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**MDPI and ACS Style**

Regassa, Y.; Gari, J.; Lemu, H.G.
Composite Overwrapped Pressure Vessel Design Optimization Using Numerical Method. *J. Compos. Sci.* **2022**, *6*, 229.
https://doi.org/10.3390/jcs6080229

**AMA Style**

Regassa Y, Gari J, Lemu HG.
Composite Overwrapped Pressure Vessel Design Optimization Using Numerical Method. *Journal of Composites Science*. 2022; 6(8):229.
https://doi.org/10.3390/jcs6080229

**Chicago/Turabian Style**

Regassa, Yohannes, Jema Gari, and Hirpa G. Lemu.
2022. "Composite Overwrapped Pressure Vessel Design Optimization Using Numerical Method" *Journal of Composites Science* 6, no. 8: 229.
https://doi.org/10.3390/jcs6080229