# Design and Analysis of a Lightweight Composite Shipping Container Made of Carbon Fiber Laminates

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

_{2}emissions by at least 50% by 2050 compared with 2008. Patricksson and Erikstad [26] assessed sulfur emissions to minimize total costs, with aggregated power requirements and emission regulations serving as constraints to the problem.

_{x}, SO

_{x}, CO, CO

_{2}, and PM emissions by 76.8%, 89%, 55%, 18.1%, and 82.6%, respectively [34].

## 3. Materials and Methods

#### 3.1. Composite Materials and Layers

#### 3.2. Static Structural Analysis

#### 3.3. Buckling Analysis

## 4. Numerical Analyses and Results

#### 4.1. Composite Layers

#### 4.2. Static Structural Analysis

#### 4.3. Composite Layers Analysis: Inverse Reserve Factor (IRF)

#### 4.4. Buckling Analysis

#### 4.5. Statistical Analysis

## 5. Conclusions

## Funding

## Conflicts of Interest

## Appendix A

Shipping Container Type | External Length | Internal Length | External Height | Internal Height | External Width | Internal Width |
---|---|---|---|---|---|---|

20-foot | 20-foot | 19 ft 9 inches | 8 ft 6 inches | 7 ft 10 inches | 8 ft | 7 ft 10 inches |

6.09 m | 6.01 m | 2.59 m | 2.39 m | 2.44 m | 2.34 m | |

40-foot | 40-foot | 39 ft 9 inches | 8 ft 6 inches | 7 ft 10 inches | 8 ft | 7 ft 10 inches |

12.18 m | 12.11 m | 2.59 m | 2.39 m | 2.44 m | 2.34 m | |

20-foot high cube | 20-foot | 19 ft 9 inches | 9 ft 6 inches | 8 ft 10 inches | 8 ft | 7 ft 10 inches |

6.09 m | 6.01 m | 2.90 m | 2.69 m | 2.44 m | 2.3 m | |

40-foot high cube | 40-foot | 39 ft 9 inches | 9 ft 6 inches | 8 ft 10 inches | 8 ft | 7 ft 10 inches |

12.18 m | 12.11 m | 2.90 m | 2.69 m | 2.44 m | 2.34 m |

Length: | 10-Foot | 20-Foot | 40-Foot |
---|---|---|---|

Cubic capacity | 15.95 cubic meters | 33.2 cubic meters | 67.59 cubic meters |

563.3 cubic feet | 1173 cubic feet | 2387 cubic feet |

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

Density $\rho $ | 0.00149 g ${\mathrm{mm}}^{-3}$ |

Elastic modulus of longitudinal direction ${E}_{1}$ (Young’s Modulus X direction) | 1,121,000 MPa |

Elastic modulus in transverse direction ${E}_{2}$ (Young’s Modulus Y direction) | 8600 MPa |

Young’s Modulus Z direction | 8600 MPa |

Poisson’s ratio ${\upsilon}_{12}$ (Poisson’s Ratio XY) | 0.27 |

Poisson’s Ratio YZ | 0.4 |

Poisson’s Ratio XZ | 0.27 |

Shear modulus ${G}_{12}$ (Shear Modulus XY) | 4700 MPa |

Shear Modulus YZ | 3100 MPa |

Shear Modulus XZ | 4700 MPa |

Longitudinal tensile strength ${X}_{t}$ | 2231 MPa |

Longitudinal compressive strength ${X}_{c}$ | 1082 MPa |

Transverse tensile strength ${Y}_{t}$ | 29 MPa |

Transverse compressive strength ${Y}_{c}$ | 100 MPa |

Shear strength $S$ | 60 MPa |

## References

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**Figure 1.**(

**a**) The exterior view of a standard 40-foot ISO container made of steel, and (

**b**) the interior view of the structural components of a container.

**Figure 2.**Properties of carbon fibers. (

**a**) Epoxy carbon unidirectional (UD) (230 $\mathrm{GPa}$), (

**b**) quasi-isotropic laminates without honeycomb (230 $\mathrm{GPa}$), and (

**c**) quasi-isotropic laminates with honeycomb (230 $\mathrm{GPa}$).

**Figure 3.**(

**a**) The quasi-isotropic laminates with a honeycomb layer (plies with 0°, 90°, +45°, −45°, 0°, 90°; one layer of honeycomb; and plies with 90°, 0°, −45, +45, 90°, 0°), (

**b**) quasi-isotropic laminates with honeycomb in the middle, (

**c**) quasi-isotropic laminates without honeycomb (0°, 90°, +45°, −45°, 0°, 90°), (

**d**) quasi-isotropic laminates without honeycomb, (

**e**) a sample honeycomb unit cell, and (

**f**) a sample honeycomb layer.

**Figure 4.**(

**a**) Corner posts, corner fittings, bars, and rails are highlighted. (

**b**) 40-foot composite container. Thicknesses of composite layers are displayed.

**Figure 5.**Force directions. (

**a**) Stacking: ~100 tons (1000 kN) negative Z direction, (

**b**) lifting: ~100 tons (1000 kN) plus Z direction, (

**c**) stacking: ~35 tons (350 kN) negative Z direction, and (

**d**) lifting: ~30 tons (300 kN) plus Z direction.

**Figure 6.**(

**a**) Stacking: Total deformation (1000 kN negative z direction), (

**b**) stacking: Von Mises stress distribution (1000 kN negative z direction), and (

**c**) lifting: Total deformation (1000 kN positive z direction).

**Figure 7.**Inverse reserve factor (IRF) analysis results. (

**a**) The corners are under ~100 tons of load (1000 kN negative z direction), (

**b**) IRF of the corner fitting: the corner is under ~100 tons of load (1000 kN negative z direction), and (

**c**) IRF of the corner fitting: under ~100 tons pulling load (1000 kN positive z direction).

**Figure 8.**Each corner is under ~100 tons of load and the phenomena is exaggerated 320 times. (

**a**) Buckling mode 1, (

**b**) buckling mode 2, and (

**c**) buckling mode 3.

**Figure 10.**(

**a**) Lifting: Positive Z direction inverse reserve factor (IRF) and (

**b**) stacking: Negative Z direction IRF.

Length | 10-Foot | 20-Foot | 40-Foot |
---|---|---|---|

Maximum gross weight | 11,300 kg | 30,480 kg | 30,400 kg |

24,910 lbs | 67,200 lbs | 67,200 lbs | |

Tare weight | 1300 kg | 2160 kg | 3750 kg |

2870 lbs | 4760 lbs | 8270 lbs | |

Payload (net weight) | 10,000 kg | 28,320 kg | 26,730 kg |

22,040 lbs | 62,440 lbs | 58,930 lbs |

Components of the Composite Container | Quantity of Composite Layers |
---|---|

All corner posts, all rails, and all cross members | 2 $\times $ [quasi-isotropic laminates (6 layers + one honeycomb + 6 layers)] |

Panels | 1 $\times $ [quasi-isotropic laminates (6 layers + one honeycomb + 6 layers)] |

Corner fittings | 2 $\times $ [quasi-isotropic laminates (6 layers + one honeycomb + 6 layers)] and 30 $\times $ [quasi-isotropic laminates (6 layers without honeycomb)] |

Section | Area and Weight | Value |
---|---|---|

All elements (including panels) | Covered area | 155.72 ${\mathrm{m}}^{2}$ |

Modeling ply area | 195.74 ${\mathrm{m}}^{2}$ | |

Production ply area | 212.67 ${\mathrm{m}}^{2}$ | |

Weight | 822.87 $\mathrm{kg}$ | |

All corner posts, all rails, all cross members, and all corner fittings (excluding panels) | Covered area | 39.44 ${\mathrm{m}}^{2}$ |

Modeling ply area | 79.46 ${\mathrm{m}}^{2}$ | |

Production ply area | 96.40 ${\mathrm{m}}^{2}$ | |

Weight | 351.25 $\mathrm{kg}$ |

${\mathit{\psi}}_{\mathit{i}}$ | ${\mathit{\lambda}}_{\mathit{i}}$ |
---|---|

Mode 1 | $-0.11$ |

Mode 2 | $-0.09$ |

Mode 3 | $+0.26$ |

**Table 5.**Descriptive statistics of total deformations under various loads in the +Z or −Z direction.

Load Type | Load and Direction | Valid N (Nodes) | Mean (mm) | Minimum (mm) | Maximum (mm) | Std. dev. |
---|---|---|---|---|---|---|

Lifting | 30 t, positive Z | 19596 | 0.732 | 0.000 | 1.542 | 0.415 |

100 t, positive Z | 19596 | 2.441 | 0.000 | 5.140 | 1.382 | |

Stacking | 35 t, negative Z | 19596 | 0.854 | 0.000 | 1.799 | 0.484 |

100 t, negative Z | 19596 | 2.441 | 0.000 | 5.140 | 1.382 |

Direction | Positive Z (Lifting Load) | Negative Z (Stacking Load) | ||
---|---|---|---|---|

Load | 30 t | 100 t | 35 t | 100 t |

Count | 19,596 | 19,596 | 19,596 | 19,596 |

Average | 0.73 | 2.44 | 0.85 | 2.44 |

Standard deviation | 0.41 | 1.38 | 0.48 | 1.38 |

Coefficient of variation | 56.61% | 56.61% | 56.61% | 56.61% |

Minimum | 0.00 | 0.00 | 0.00 | 0.00 |

Maximum | 1.54 | 5.14 | 1.80 | 5.14 |

Range | 1.54 | 5.14 | 1.80 | 5.14 |

Std. skewness | 4.62 | 4.62 | 4.62 | 4.62 |

Std. kurtosis | −38.05 | −38.05 | −38.05 | −38.05 |

Test num. | Load Direction | Statistic | Value |
---|---|---|---|

1 | Distributions of 30 t and 100 t loads in the positive Z direction (lifting) | Estimated overall statistic DN | 0.76 |

Two-sided large sample K-S statistic | 75.49 | ||

Approximate p-value | 0.00 | ||

2 | Distributions of 35 t and 100 t loads in the negative Z direction (stacking) | Estimated overall statistic DN | 0.64 |

Two-sided large sample K-S statistic | 62.99 | ||

Approximate p-value | 0.00 |

Test num. | Comparison of Medians | Test | Value |
---|---|---|---|

1 | 30 t and 100 t lifting loads in the positive Z direction | Median of sample 1 | 0.58531 |

Median of sample 2 | 1.951 | ||

Average rank of sample 1 | 12,004.3 | ||

Average rank of sample 2 | 27,188.7 | ||

W | 340778000 | ||

p-value | 0.00 | ||

2 | 35 t and 100 t stacking loads in the negative Z direction | Median of sample 1 | 0.68287 |

Median of sample 2 | 1.951 | ||

Average rank of sample 1 | 12,702.5 | ||

Average rank of sample 2 | 26,490.5 | ||

W | 327096000 | ||

p-value | 0.00 |

Load Type | Load and Direction | Valid N | Mean | Minimum | Maximum | Std. Dev. |
---|---|---|---|---|---|---|

Lifting | 30 t, positive Z | 19,721 | 0.045 | 0.000 | 1.046 | 0.070 |

100 t, positive Z | 19,721 | 0.149 | 0.000 | 3.485 | 0.234 | |

Stacking | 35 t, negative Z | 19,721 | 0.026 | 0.000 | 0.925 | 0.046 |

100 t, negative Z | 19,721 | 0.074 | 0.000 | 2.643 | 0.131 |

**Table 10.**Frequency table: 30 t +Z inverse reserve factor (IRF), Kolmogorov–Smirnov (K-S) d = 0.28266, p < 0.01.

Node Count | Cumulative Count of Nodes | % of Valid | Cumulative % of Valid | % of All Cases | Cumulative % of All Cases | |
---|---|---|---|---|---|---|

$0$$<$$x$$\le $$0.722\times {10}^{-15}$ | 149 | 149 | 0.756 | 0.756 | 0.756 | 0.756 |

$0.722\times {10}^{-15}$$x\le 0.2$ | 19,121 | 19,270 | 96.958 | 97.713 | 96.958 | 97.713 |

$0.2$$<$$x$$\le $$0.4$ | 394 | 19,664 | 1.998 | 99.711 | 1.998 | 99.711 |

$0.4$$<$$x$$\le $$0.6$ | 41 | 19,705 | 0.208 | 99.919 | 0.208 | 99.919 |

$0.6$$<$$x$$\le $$0.8$ | 11 | 19,716 | 0.056 | 99.975 | 0.056 | 99.975 |

$0.8$$<$$x$$\le $$1$ | 4 | 19,720 | 0.020 | 99.995 | 0.020 | 99.995 |

$1$$<$$x$$\le $$1.2$ | 1 | 19,721 | 0.005 | 100 | 0.005 | 100 |

Missing | 0 | 19,721 | 0 | 0 | 100 |

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**MDPI and ACS Style**

Yildiz, T.
Design and Analysis of a Lightweight Composite Shipping Container Made of Carbon Fiber Laminates. *Logistics* **2019**, *3*, 18.
https://doi.org/10.3390/logistics3030018

**AMA Style**

Yildiz T.
Design and Analysis of a Lightweight Composite Shipping Container Made of Carbon Fiber Laminates. *Logistics*. 2019; 3(3):18.
https://doi.org/10.3390/logistics3030018

**Chicago/Turabian Style**

Yildiz, Turkay.
2019. "Design and Analysis of a Lightweight Composite Shipping Container Made of Carbon Fiber Laminates" *Logistics* 3, no. 3: 18.
https://doi.org/10.3390/logistics3030018