Multi-Objective Robust Design Optimization for Crashworthiness Enhancement of Hybrid 2D Triaxially Braided Composite Tube Using Evolutionary Algorithms
Abstract
:1. Introduction
2. Analytical Model of 2DTBC
2.1. Local Stiffness Analysis
2.2. Macroscopic Stiffness
2.3. Progressive Ply Failure Analysis
- (1)
- Increase the external load until one of the four plies fails according to the Tsai–Wu criterion;
- (2)
- Recalculate the local stiffness of this ply and the global stiffness matrix using degraded elastic constants determined using different failure modes;
- (3)
- Determine the local stress of each ply again from Equation (30);
- (4)
- Continue to increase the load gradually until a new ply fails or the failure mode of the failed ply changes from the fiber failure to matrix failure;
- (5)
- Repeat steps 2–4 until all four plies of the 2DTBC fail;
- (6)
- The maximum load is extracted as the ultimate strength of the 2DTBC.
3. Optimization
3.1. Model Description
3.2. Definition of the Crashworthiness Optimization Problem
3.2.1. Design Variables and Objective Functions
- Vft: The total fiber volume fraction.
- Vcr: The relative volume fraction of carbon fiber in the total fiber volume fraction.
- : The braid angle.
3.2.2. Problem Formulations
- (1)
- Crashworthiness optimization issues:
- (2)
- Lightweight design of structure:
3.3. Solution
4. Results and Discussion
4.1. Error Evaluation of the Surrogate Model
4.2. Parametric Analysis
4.3. Pareto Optimal Solutions
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value | Parameter | Value |
---|---|---|---|
Carbon longitudinal Young’s modulus | 255 Gpa | Matrix (epoxy) Young’s modulus | 3.056 Gpa |
Carbon transverse Young’s modulus | 15 Gpa | Matrix Poisson’s ratio | 0.3 |
Carbon longitudinal shear modulus | 24 Gpa | Matrix tensile strength | 74 MPa |
Carbon transverse shear modulus | 5 Gpa | Matrix compression strength | 241 Mpa |
Carbon longitudinal Poisson’s ratio | 0.14 | Matrix shear strength | 60 Mpa |
Carbon longitudinal tensile strength | 4400 Mpa | Carbon fiber volume fraction | 39.2% |
Carbon longitudinal compression strength | 2470 Mpa | Glass fiber volume fraction | 12.8% |
Glass Young’s modulus | 73 Gpa | Matrix volume fraction | 48% |
Glass Poisson’s ratio | 0.18 | Braid angle | |
Glass tensile/compression strength | 2600 Mpa | Braid tow amplitude | 0.701 mm |
Glass shear strength | 50 Mpa | Braid tow wavelength | 14.03 mm |
Exx/GPa | Eyy/GPa | Gxy/GPa | ν12 | Xt/MPa | Xc/MPa | Yt/MPa | Yc/MPa | Sxy/MPa | |
---|---|---|---|---|---|---|---|---|---|
Analytical model | 76.4 | 8.29 | 5.37 | 0.32 | 1280 | 392.4 | 52.3 | 122 | 97 |
Experiments | 74.5 | 9.65 | 5.74 | 0.29 | 1090 | 416.2 | 40.8 | 125.4 | 91.2 |
Relative error | 2.5% | 14.1% | 6.4% | 10.3% | 17.4% | 5.7% | 14.8% | 2.7% | 6.3% |
Carbon Fiber | Glass Fiber | Matrix | |
---|---|---|---|
Density (kg/m3) | 1800 | 2460 | 1090 |
Cost ($/Kg) | 35.9 | 24.5 | 6.2 |
Design Variables | Lower Bound | Upper Bound |
---|---|---|
Vft | 0.3 | 0.7 |
Vcr | 0.1 | 0.9 |
10 | 85 |
Vft | Vcr | SEA (J/g) | P (KN) | ||
---|---|---|---|---|---|
Initial design | 0.52 | 0.75 | 45 | 23.23 | 36.64 |
Crashworthiness Optimization | 0.43 | 0.32 | 43.89 | 28.52 | 30.58 |
Improvement | 22.9% | 16.45% |
Vft | Vcr | Material Cost ($/cm3) | DenSity (g/cm3) | ||
---|---|---|---|---|---|
Initial design | 0.52 | 0.75 | 45 | 121.80 | 1.43 |
Lightweight design | 0.33 | 0.51 | 44.62 | 87.25 | 1.35 |
Improvement | 28.37% | 6.72% |
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Sun, D.; Jiao, Y.; Tian, Y.; Gong, Y.; Li, L.; Ning, H. Multi-Objective Robust Design Optimization for Crashworthiness Enhancement of Hybrid 2D Triaxially Braided Composite Tube Using Evolutionary Algorithms. Polymers 2024, 16, 2457. https://doi.org/10.3390/polym16172457
Sun D, Jiao Y, Tian Y, Gong Y, Li L, Ning H. Multi-Objective Robust Design Optimization for Crashworthiness Enhancement of Hybrid 2D Triaxially Braided Composite Tube Using Evolutionary Algorithms. Polymers. 2024; 16(17):2457. https://doi.org/10.3390/polym16172457
Chicago/Turabian StyleSun, Dongyang, Yudu Jiao, Yuanhao Tian, Youkun Gong, Leilei Li, and Huiming Ning. 2024. "Multi-Objective Robust Design Optimization for Crashworthiness Enhancement of Hybrid 2D Triaxially Braided Composite Tube Using Evolutionary Algorithms" Polymers 16, no. 17: 2457. https://doi.org/10.3390/polym16172457