Performance Study of Origami Crash Tubes Based on Energy Dissipation History
Abstract
:1. Introduction
2. Numerical Simulation
2.1. 3D Geometry Model
2.2. Finite Element Simulation
Algorithm 1: Compute 3D spatial coordinates of the vertex |
1: Input: total length ; list of the heights for each floor ; number of layers ; 2: number of prefolded points in each layer ;list of edge lengths for each layer . 3: Output: 4: Initialize an empty array with size 5: for each layer do 6: Calculate the coordinate values of , and , 7: 8: end for |
Algorithm 2 Data reconfiguration ( represents the transpose of row m for the array, the same as below. Permutation () is a method to exchange the order of alignment, for example: array .) |
1: Input: the spatial coordinates array of ; number of layers ; 2: number of prefolded points in each layer . 2: Output: the array 3: Initialize an empty array with size 4: for -1 do 5: Initialize an empty array with size 6: 7: 8: end for |
2.3. Numerical Simulation Verification and Energy Absorption Evaluation
3. Crushing Force–Displacement History Curve Clustering
3.1. Clustering Method
3.1.1. Similarity Measurement between Different Curves
3.1.2. Unsupervised Learning-Clustering Method
Algorithm 3 Based on K-Means time series clustering ( is the weight of each datum within the same cluster.) |
1: Input: All time series data and number of clusters k 2: Output: The k clusters of data after clustering 3: Randomly initialize clustering centers , by using k-means++ [63] algorithm 4: repeat 5: for do 6: Calculate the distance between each data and each clustering center according to Equation 12 7: and assign the data to the cluster whose distance is closest to the clustering center. 8: for do 10: recalculate the clustering center of data . Then update clustering center. 11: untill The clustering center does not change |
3.1.3. Number of Clusters Setting
3.2. Data and Operating Environment
4. Results and Analysis
4.1. Number of Clusters Analysis
4.2. Energy Absorption Performance Analysis of Each Cluster after Clustering
4.3. Verification in Terms of Clustering Quality
4.4. Crushing Process Analysis of Each Cluster after Clustering
5. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Model | Cluster | Collapse | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Reduction | Increase | Mode | ||||||||
D2-1 | 30 | 30 | 30 | 30 | 19.3 | - | 20.0 | - | 3 | D |
D2-2 | 40 | 20 | 40 | 20 | 12.6 | 34.8% | 15.7 | −21.5% | 4 | M |
D2-3 | 45 | 30 | 15 | 30 | 7.9 | 59.0% | 19.3 | −3.6% | 5 | M |
D2-4 | 30 | 45 | 30 | 15 | 11.5 | 40.3% | 16.8 | −16.0% | 6 | M |
D2-5 | 30 | 45 | 15 | 30 | 8.0 | 58.3% | 16.7 | −16.6% | 8 | M |
D2-6 | 45 | 15 | 40 | 20 | 8.2 | 57.6% | 18.8 | −6.2% | 4 | M |
D2-7 | 40 | 20 | 45 | 15 | 12.5 | 35.3% | 15.0 | −25.3% | 4 | M |
D2-8 | 30 | 40 | 30 | 20 | 19.3 | −0.3% | 18.1 | −9.5% | 6 | M |
D2-9 | 40 | 30 | 20 | 30 | 12.0 | 37.9% | 17.6 | −12.3% | 2 | M |
D2-10 | 20 | 45 | 40 | 15 | 12.5 | 34.9% | 21.0 | 4.7% | 1 | M |
D2-11 | 45 | 20 | 15 | 40 | 7.7 | 60.0% | 19.8 | −1.0% | 1 | M |
D2-12 | 45 | 45 | 15 | 15 | 8.0 | 58.6% | 19.9 | −0.6% | 5 | M |
D2-13 | 40 | 20 | 30 | 30 | 12.2 | 36.8% | 16.9 | −15.5% | 4 | M |
D2-14 | 30 | 30 | 40 | 20 | 20.2 | −4.8% | 18.2 | −9.3% | 3 | M |
D2-15 | 45 | 40 | 15 | 20 | 7.9 | 59.2% | 18.9 | −5.8% | 5 | M |
D2-16 | 45 | 40 | 20 | 15 | 10.5 | 45.5% | 17.9 | −10.5% | 8 | M |
D2-17 | 40 | 45 | 20 | 15 | 10.5 | 45.4% | 18.6 | −7.4% | 8 | M |
D2-18 | 40 | 45 | 15 | 20 | 7.9 | 59.1% | 17.4 | −13.3% | 8 | M |
D2-19 | 40 | 15 | 45 | 20 | 8.2 | 57.6% | 18.4 | −7.9% | 2 | M |
D2-20 | 40 | 30 | 30 | 20 | 17.9 | 7.4% | 19.4 | −3.1% | 6 | M |
D2-21 | 40 | 40 | 20 | 20 | 12.0 | 37.9% | 17.0 | −15.1% | 2 | M |
D2-22 | 40 | 20 | 15 | 45 | 7.8 | 59.4% | 19.9 | −0.6% | 7 | M |
D2-23 | 20 | 40 | 45 | 15 | 12.8 | 33.6% | 19.7 | −1.8% | 3 | M |
D2-24 | 40 | 20 | 20 | 40 | 10.9 | 43.3% | 19.1 | −4.7% | 2 | M |
D2-25 | 20 | 40 | 40 | 20 | 20.1 | −4.3% | 18.5 | −7.6% | 8 | M |
D2-26 | 45 | 15 | 15 | 45 | 7.5 | 60.9% | 18.9 | −5.4% | 5 | M |
D2-27 | 15 | 45 | 45 | 15 | 12.6 | 34.8% | 20.0 | −0.3% | 5 | M |
D2-28 | 45 | 15 | 30 | 30 | 8.0 | 58.4% | 19.9 | −0.7% | 7 | M |
D2-29 | 30 | 30 | 45 | 15 | 12.7 | 33.9% | 18.9 | −5.8% | 6 | M |
D2-30 | 45 | 30 | 30 | 15 | 11.4 | 40.7% | 20.7 | 3.5% | 6 | M |
D2-31 | 45 | 15 | 45 | 15 | 8.2 | 57.5% | 17.8 | −11.4% | 4 | M |
D2-32 | 30 | 20 | 40 | 30 | 12.3 | 36.1% | 16.3 | −18.4% | 2 | M |
D2-33 | 45 | 20 | 40 | 15 | 12.1 | 37.3% | 15.0 | −25.2% | 4 | M |
Model | IES | ECR | |||
---|---|---|---|---|---|
(a) Cluster 1 | |||||
D2-10 | 12.5 | 21.0 | 2699.57 | 1.67 | 9.39e8 |
D2-11 | 7.7 | 19.8 | 3177.53 | 2.57 | 9.39e8 |
(b) Cluster 2 | |||||
D2-9 | 12.0 | 17.6 | 1955.91 | 1.47 | 7.83e8 |
D2-32 | 12.3 | 16.3 | 2259.96 | 1.33 | 1.64e9 |
D2-21 | 12.0 | 17.0 | 1600.84 | 1.42 | 1.72e9 |
D2-19 | 8.2 | 18.4 | 3108.94 | 2.26 | 1.73e9 |
D2-24 | 10.9 | 19.1 | 1323.27 | 1.75 | 2.31e9 |
(c) Cluster 3 | |||||
D2-1 | 19.3 | 20.0 | 1140.67 | 1.04 | 8.79e8 |
D2-14 | 20.2 | 18.2 | 1301.61 | 0.90 | 1.05e9 |
D2-23 | 12.8 | 19.7 | 3365.79 | 1.54 | 1.29e9 |
(d) Cluster 4 | |||||
D2-2 | 12.6 | 15.7 | 2200.32 | 1.25 | 6.63e8 |
D2-7 | 12.5 | 15.0 | 1478.99 | 1.20 | 1.15e9 |
D2-33 | 12.1 | 15.0 | 1741.56 | 1.24 | 1.60e9 |
D2-31 | 8.2 | 17.8 | 3480.01 | 2.17 | 1.66e9 |
D2-13 | 12.2 | 16.9 | 2108.07 | 1.39 | 1.77e9 |
D2-6 | 8.2 | 18.8 | 3368.71 | 2.30 | 1.85e9 |
(e) Cluster 5 | |||||
D2-12 | 8.0 | 19.9 | 1324.74 | 2.49 | 8.69e8 |
D2-27 | 12.6 | 20.0 | 2089.04 | 1.59 | 1.56e9 |
D2-15 | 7.9 | 18.9 | 2382.30 | 2.40 | 2.00e9 |
D2-3 | 7.9 | 19.3 | 2962.28 | 2.44 | 2.38e9 |
D2-26 | 7.5 | 18.9 | 1325.05 | 2.51 | 2.63e9 |
(f) Cluster 6 | |||||
D2-29 | 12.7 | 18.9 | 3532.30 | 1.48 | 2.63e8 |
D2-20 | 17.9 | 19.4 | 1281.86 | 1.09 | 2.04e9 |
D2-8 | 19.3 | 18.1 | 1124.70 | 0.94 | 3.16e9 |
D2-4 | 11.5 | 16.8 | 3188.97 | 1.46 | 3.67e9 |
D2-30 | 11.4 | 20.7 | 2956.80 | 1.81 | 5.13e9 |
(g) Cluster 7 | |||||
D2-28 | 8.0 | 19.9 | 3011.79 | 2.48 | 2.04e9 |
D2-22 | 7.8 | 19.9 | 2975.39 | 2.54 | 2.04e9 |
(h) Cluster 8 | |||||
D2-16 | 10.5 | 17.9 | 1513.66 | 1.71 | 7.00e8 |
D2-17 | 10.5 | 18.6 | 1441.57 | 1.76 | 8.27e8 |
D2-5 | 8.0 | 16.7 | 3545.03 | 2.08 | 8.83e8 |
D2-18 | 7.9 | 17.4 | 2556.22 | 2.21 | 2.08e9 |
D2-25 | 20.1 | 18.5 | 1517.19 | 0.92 | 2.57e9 |
Model | D | IES | ECR | Cluster | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Reduction | Increase | |||||||||||
D2-1 | 30 | 30 | 30 | 30 | 0 | 19.3 | - | 20 | 1140.67 | 1.04 | - | |
D2-34 | 31.5 | 28.5 | 31.5 | 28.5 | 3 | 18.87 | 2.2% | 18.24 | −8.8% | 1199.12 | 0.97 | 1 |
D2-35 | 33 | 27 | 33 | 27 | 6 | 18.07 | 6.4% | 17.33 | −13.4% | 1331.44 | 0.96 | 1 |
D2-36 | 34.5 | 25.5 | 34.5 | 25.5 | 9 | 16.98 | 12.0% | 16.63 | −16.9% | 1532.17 | 0.98 | 1 |
D2-37 | 36 | 24 | 36 | 24 | 12 | 15.88 | 17.7% | 16.00 | −20.0% | 1640.95 | 1.01 | 1 |
D2-38 | 37.5 | 22.5 | 37.5 | 22.5 | 15 | 14.60 | 24.3% | 15.32 | −23.4% | 1828.22 | 1.05 | 2 |
D2-39 | 39 | 21 | 39 | 21 | 18 | 13.45 | 30.3% | 15.29 | −23.6% | 2095.99 | 1.14 | 2 |
D2-40 | 40.5 | 19.5 | 40.5 | 19.5 | 21 | 12.22 | 36.7% | 16.22 | −18.9% | 2277.38 | 1.33 | 2 |
D2-41 | 42 | 18 | 42 | 18 | 24 | 10.93 | 43.3% | 16.16 | −19.2% | 2644.38 | 1.48 | 2 |
D2-42 | 43.5 | 16.5 | 43.5 | 16.5 | 27 | 9.62 | 50.1% | 17.04 | −14.8% | 3390.00 | 1.77 | 2 |
D2-43 | 45 | 15 | 45 | 15 | 30 | 8.21 | 57.5% | 17.89 | −10.5% | 3485.15 | 2.18 | 3 |
D2-44 | 46.5 | 13.5 | 46.5 | 13.5 | 33 | 6.46 | 66.6% | 19.15 | −4.2% | 3723.75 | 2.97 | 3 |
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Zhang, P.; Sun, Z.; Wang, H.; Xiang, X. Performance Study of Origami Crash Tubes Based on Energy Dissipation History. Energies 2022, 15, 3109. https://doi.org/10.3390/en15093109
Zhang P, Sun Z, Wang H, Xiang X. Performance Study of Origami Crash Tubes Based on Energy Dissipation History. Energies. 2022; 15(9):3109. https://doi.org/10.3390/en15093109
Chicago/Turabian StyleZhang, Peng, Zuoyu Sun, Hui Wang, and Xinmei Xiang. 2022. "Performance Study of Origami Crash Tubes Based on Energy Dissipation History" Energies 15, no. 9: 3109. https://doi.org/10.3390/en15093109