# Crashworthiness Optimization Design of Aluminum Alloy Thin-Walled Triangle Column Based on Bioinspired Strategy

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^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Models and Validation

#### 2.1. Process Overview

#### 2.2. Bioinspired Strategy

_{i}in Euclidean XY plane is defined as:

#### 2.3. Geometry Model

#### 2.4. FE Models and Validation

_{e}and the side length D

_{0}of the 0th fractal column are 300 mm and 100 mm, respectively. The thickness t

_{0}is set to 2 mm. The bottom of the column is supported by a rigid body. A rigid impactor is moving to the top end of the column with a constant speed of 5 mm/min. The total collapse distance is 150 mm.

## 3. Theoretical Model Establishment

_{m}denotes the average crush force, H is the half fold length, η represents the effective crushing distance coefficient. E

_{bending}and E

_{membrane}are the bending dissipation energy and the membrane dissipation energy respectively.

_{e}is the experimental mean crush force, S

_{d}is the effective crushing length, P(x) is the crushing force at the distance of x.

_{0}= σ

_{0}t

^{2}/4 represents the wholly plastic bending moment per unit width, b is the panel width, p is the number of the panel in the multi-cell column. σ

_{0}refers to the flow stress of the material, and t is the thickness of the column.

_{y}, σ

_{u}, are the yield stress of the material and the ultimate stress of the material respectively. n is power law exponent.

_{0}and the bending energy is calculated as:

_{1}and the bending energy is calculated as:

_{2}and the bending energy is calculated as:

## 4. Crashworthiness Comparison

## 5. Parametric Study of Crashworthiness

#### 5.1. Collapse Modes

_{0}takes the value of 80 mm, 100 mm, and 120 mm. Column height H

_{e}takes the value of 250 mm, 300 mm, and 350 mm. Thickness t

_{0}takes the value of 1.5 mm, 2 mm, 2.5 mm. The relationship of between design variables and the collapse mode is illustrated in Figure 10. Figure 10a shows the sampling points of the three parameters. Figure 10b shows the collapse mode diagram of 0th-order column. Figure 10c shows collapse mode diagram of 1st-order column. Figure 10d shows collapse mode diagram of the 2nd-order column. It can be found that the fractal order has a significant influence on the collapse mode of the FTTC. With the increase of fractal order, FTTC has an unstable tendency. Moreover, increasing the thickness and side length contributes to a stable collapse.

#### 5.2. Effect of Thickness

_{0}is the 0th-order wall thickness, t

_{1}is the 1st-order wall thickness, and t

_{2}is the 2nd-order wall thickness, as shown in Figure 11. t

_{0}is set 0.889 mm as the initial value, and the factor design of five levels (0.756 mm, 0.822 mm, 0.889 mm, 0.956 mm, 1.022 mm) is utilized to sample the design space of t

_{1}, and t

_{2}.

_{1}and φ

_{2}, the bigger SEA and PCF. The slopes are steeper along the φ

_{1}axis. Accordingly, it can be summarized that the wall thickness change between 0th-order and 1st-order has a bigger effect on the SEA and PCF.

## 6. Conclusions

_{0}, it shows a tendency to transfer from the unstable to stable, whereas the change of parameter H

_{e}shows the opposite trend.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 6.**(

**a**) Photograph of the experiment set-up, (

**b**) deformed shapes of the specimen, and (

**c**) comparison of force-displacement.

**Figure 10.**(

**a**) Sampling points of the three parameters, (

**b**) collapse mode diagram of 0th-order column, (

**c**) collapse mode diagram of 1st-order column, (

**d**) collapse mode diagram of 2nd-order column.

**Figure 12.**(

**a**) The relationship between SEA and two coefficients, and (

**b**) the relationship between PCF and two coefficients.

Order n | Strategies | Section | Side Length | Side Number | Sides Length | Thickness |
---|---|---|---|---|---|---|

D | Q | L | t | |||

0th | D_{0} | 3 | 3D_{0} | t_{0} | ||

1st | D_{0}/2 | 3^{2} | 3^{2}D_{0}/2 | 2t_{0}/3 | ||

2nd | D_{0}/4 | 3^{3} | 3^{3}D_{0}/4 | 4t_{0}/9 |

Properties | Value |
---|---|

Density (kg/m^{3}) | 2700 |

Young’s modulus (GPa) | 68.9 |

Poisson’s ratio | 0.33 |

Initial yield stress (MPa) | 68.8 |

Ultimate stress (MPa) | 134.2 |

Power law exponent | 0.18 |

Rupture strain | 0.19 |

Indicators | Experiment | FEA | Relative Error |
---|---|---|---|

EA (J) | 2053.9 | 1793.01 | 12.7% |

SEA (J/kg) | 4226.2 | 3689.3 | 12.7% |

MCF (kN) | 14.65 | 12.83 | 12.4% |

Order n | Side Length (mm) | Height (mm) | Thickness (mm) |
---|---|---|---|

0 | 100 | 300 | 2.000 |

1 | 50 | 300 | 1.333 |

2 | 25 | 300 | 0.889 |

Order n | MCF (kN) | Theoretical (kN) | Relative Error (%) |
---|---|---|---|

0th | 12.76 | 12.27 | 3.84 |

1st | 17.00 | 18.38 | 7.51 |

2nd | 24.21 | 27.73 | 14.54 |

Indicators | 0th-Order FTTC | 1st-Order FTTC | 2nd-Order FTTC |
---|---|---|---|

SEA (kJ/kg) | 3.94 | 5.25 | 7.47 |

MCF (kN) | 12.76 | 17.00 | 24.2 |

CFE (%) | 60.42 | 70.36 | 71.56 |

PCF (kN) | 21.12 | 24.16 | 33.83 |

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**MDPI and ACS Style**

Li, K.; Feng, Y.; Gao, Y.; Zheng, H.; Qiu, H.
Crashworthiness Optimization Design of Aluminum Alloy Thin-Walled Triangle Column Based on Bioinspired Strategy. *Materials* **2020**, *13*, 666.
https://doi.org/10.3390/ma13030666

**AMA Style**

Li K, Feng Y, Gao Y, Zheng H, Qiu H.
Crashworthiness Optimization Design of Aluminum Alloy Thin-Walled Triangle Column Based on Bioinspired Strategy. *Materials*. 2020; 13(3):666.
https://doi.org/10.3390/ma13030666

**Chicago/Turabian Style**

Li, Kangjie, Yixiong Feng, Yicong Gao, Hao Zheng, and Hao Qiu.
2020. "Crashworthiness Optimization Design of Aluminum Alloy Thin-Walled Triangle Column Based on Bioinspired Strategy" *Materials* 13, no. 3: 666.
https://doi.org/10.3390/ma13030666