# Prediction of Vehicle Crashworthiness Parameters Using Piecewise Lumped Parameters and Finite Element Models

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Data and Signal Filtering

#### 2.2. Piecewise Linear Lumped Parameters Model

#### 2.3. LPM Estimation and Calibration Scheme Using the Genetic Algorithm

#### 2.4. Finite Element Analysis

- Number of parts: 804,
- Number of nodes: 922,007,
- Number of beam elements: 10,
- Number of shell elements: 838,926,
- Number of solid elements: 134,468.

#### 2.5. Acceleration Severity Index (ASI)

- Class A: ASI $\le 1,$
- Class B: 1.0 ≤ ASI $\le 1.4,$
- Class C: 1.4 ≤ ASI $\le 1.9.$

## 3. Results

## 4. Discussion

## 5. Conclusions and future work

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Full-scale crash test of a Ford Taurus (2004 model) at 56 km/h [35].

**Figure 2.**Noisy and filtered acceleration signals for full-scale frontal crash [35].

**Figure 5.**Deformed vehicle frontal structure through finite element analysis at impact velocities of (

**a**) 40 km/h; (

**b**) 56 km/h; and (

**c**) 72 km/h.

**Figure 6.**Convergence of the objective function using genetic algorithm (

**a**) Lumped parameters model calibrated to full-scale crash test; (

**b**) Lumped parameters model calibrated to finite element model.

**Figure 7.**Displacement, velocity, and acceleration plots comparison in case of LPM calibrated to FSCT, (

**a**,

**c**,

**e**) impact velocities lower than the calibration point (56 km/h); (

**b**,

**d**,

**f**) impact velocities higher than the calibration point.

**Figure 8.**Displacement, velocity, and acceleration plots comparison in case of LPM calibrated to FEA, (

**a**,

**c**,

**e**) impact velocities lower than the calibration point (56 km/h); (

**b**,

**d**,

**f**) impact velocities higher than the calibration point.

**Figure 9.**A summary of kinematic time histories for (

**a**) LPM calibrated to FSCT; (

**b**) LPM calibrated to FEM; (

**c**) comparison between FEA and FSCT at 56 km/h.

Parameters | LPM Calibrated to FSCT | LPM Calibrated to FEM |
---|---|---|

${k}_{1}$ | 7195 N/m | 25,718 N/m |

${k}_{2}$ | 7210 N/m | 31,444 N/m |

${k}_{3}$ | 25,386 N/m | 45,476 N/m |

${k}_{4}$ | 711,060 N/m | 467,830 N/m |

${x}_{1}$ | 0.0526 m | 0.2448 m |

${x}_{2}$ | 0.1023 m | 0.2923 m |

${c}_{1}$ | 59,444 Ns/m | 80,827 Ns/m |

${c}_{2}$ | 51,590 Ns/m | 7775 Ns/m |

${c}_{3}$ | 4997 Ns/m | 38,812 Ns/m |

${c}_{4}$ | 1382 Ns/m | 5703 Ns/m |

${\dot{x}}_{1}$ | 7.0585 m/s | 4.7855 m/s |

${\dot{x}}_{2}$ | 8.9272 m/s | 8.2880 m/s |

Impact Velocities | ||||||
---|---|---|---|---|---|---|

Approaches | Parameters | 40 km/h | 48 km/h | 56 km/h^{c} | 64 km/h | 72 km/h |

FSCT | ${t}_{m}$ [s] | - | - | 0.0723 | - | - |

${C}_{m}$ [m] | - | - | 0.7551 | - | - | |

ASI [-] | - | - | 2.5 | - | - | |

LPM calibrated to FSCT | ${t}_{m}$ [s] | 0.0736 | 0.0740 | 0.0738 | 0.0741 | 0.0741 |

${C}_{m}$ [m] | 0.5373 | 0.6429 | 0.7508 | 0.8588 | 0.9653 | |

ASI [-] | 1.7 | 2.1 | 2.6 | 2.7 | 3.1 | |

FEA | ${t}_{m}$ [s] | 0.0755 | 0.0781 | 0.0801 | 0.0804 | 0.0800 |

${C}_{m}$ [m] | 0.5077 | 0.6077 | 0.7180 | 0.8331 | 0.9408 | |

ASI [-] | 1.5 | 1.8 | 2.0 | 2.3 | 2.5 | |

LPM calibrated to FEA | ${t}_{m}$ [s] | 0.0824 | 0.0825 | 0.0793 | 0.0822 | 0.0805 |

${C}_{m}$ [m] | 0.5231 | 0.6258 | 0.7108 | 0.8360 | 0.9396 | |

ASI [-] | 1.4 | 1.6 | 2.0 | 2.3 | 2.5 |

^{c}Calibration point, ${t}_{m}$ is the time at maximum dynamic crush, ${C}_{m}$ is the maximum dynamic crush and $ASI$ is the acceleration severity index. FSCT: Full-Scale Crash Test, LPM: Lumped Parameters Model, FEA: Finite Element Analysis.

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**MDPI and ACS Style**

B. Munyazikwiye, B.; Vysochinskiy, D.; Khadyko, M.; G. Robbersmyr, K.
Prediction of Vehicle Crashworthiness Parameters Using Piecewise Lumped Parameters and Finite Element Models. *Designs* **2018**, *2*, 43.
https://doi.org/10.3390/designs2040043

**AMA Style**

B. Munyazikwiye B, Vysochinskiy D, Khadyko M, G. Robbersmyr K.
Prediction of Vehicle Crashworthiness Parameters Using Piecewise Lumped Parameters and Finite Element Models. *Designs*. 2018; 2(4):43.
https://doi.org/10.3390/designs2040043

**Chicago/Turabian Style**

B. Munyazikwiye, Bernard, Dmitry Vysochinskiy, Mikhail Khadyko, and Kjell G. Robbersmyr.
2018. "Prediction of Vehicle Crashworthiness Parameters Using Piecewise Lumped Parameters and Finite Element Models" *Designs* 2, no. 4: 43.
https://doi.org/10.3390/designs2040043