Multi-Load Topology Optimization Design for the Structural Safety Maintenance of Low- and Intermediate-Level Radioactive Waste Packaging Containers in the Case of a Collision
Abstract
:1. Introduction
2. Drop Analysis of Packaging Containers
2.1. Finite Element Model
2.2. Analysis Condition
- Vertical drop (Case 1): Drop with the bottom surface and ground being horizontal.
- Center of gravity drop (Corner 1): The line connecting the center of gravity and the corner vertex is vertical to the ground.
- Center of gravity side drop (Side 1): The line connecting the center of gravity and the center of the side is vertical to the ground.
- Corner–base drop (Corner 2): The line connecting the corner and the base is horizontal to the ground.
- Edge–base drop (Side 2): The line connecting the edge and the base is horizontal to the ground.
2.3. Analysis Result
3. Multi-Load Topology Optimization
3.1. Topology Optimization
3.2. Approximate Model
3.3. Selection of Weight Criteria
3.4. Formulation of Topology Optimization
3.5. Results of Topology Optimization
4. Structural Safety Maintenance
4.1. Analysis of Topology Optimization Results
4.1.1. Corner 1 and 2 Drop Directions
4.1.2. Side 1 Drop Direction
4.1.3. Side 2 Drop Direction
4.2. Final Model Selection
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Yun, S.T. Site Selection for Low and Intermediate Level Radioactive Waste Disposal Facility in Korea. Prog. Nucl. Energy 2008, 50, 680–682. [Google Scholar] [CrossRef]
- Lee, J.; Park, S.; Ko, D.; Jang, J.; Cho, Y.; Choi, C.; Kim, D. Evaluating the Airtightness of Medium- and Low-Intermediate-Level Radioactive Waste Packaging Container through Finite Element Analysis. J. Korean Packag. Soc. 2023, 29, 203–209. [Google Scholar] [CrossRef]
- Baik, J.K.; Jung, S.W.; Son, J.W. A Study on Applying Methods of Waste Package for Decommissioning Wastes of Nuclear Power Plant. J. Energy Eng. 2022, 31, 24–33. [Google Scholar] [CrossRef]
- Park, S.O. Multi-Model Optimization Using the Equivalent Static Loads Method. Ph.D. Thesis, Hanyang University, Seoul, Republic of Korea, 2020. [Google Scholar]
- Kang, H.; Jang, J.-S.; Kim, D.-H.; Kang, J.-H.; Yoo, W.-S.; Lee, J.-W. Prediction of Impact Energy Absorption in a High Weight Drop Tester by Response Surface Methodology. J. Korean Soc. Manuf. Process Eng. 2016, 15, 44–51. [Google Scholar] [CrossRef]
- Kim, Y.I.; Park, G.J. Nonlinear Dynamic Response Structural Optimization Using Equivalent Static Loads. Comput. Methods Appl. Mech. Eng. 2010, 199, 660–676. [Google Scholar] [CrossRef]
- Kim, D.Y.; Kim, J.W.; Jang, J.S. Seismic Integrity Analysis of Radioactive Waste Containers Using the Response Spectrum Method. Trans. Korean Soc. Mech. Eng. A 2022, 46, 421–428. [Google Scholar] [CrossRef]
- Yi, R.; Zhao, Z.-L.; Feng, X.-Q.; Xie, Y.M. Structural Topology Optimization with an Adaptive Design Domain. Comput. Methods Appl. Mech. Eng. 2022, 389, 114382. [Google Scholar] [CrossRef]
- Ateshian, G.A.; Maas, S.; Weiss, J.A. Finite Element Algorithm for Frictionless Contact of Porous Permeable Media under Finite Deformation and Sliding. J. Biomech. Eng. 2010, 132, 061006. [Google Scholar] [CrossRef]
- Zang, M.; Gao, W.; Lei, Z. A Contact Algorithm for 3D Discrete and Finite Element Contact Problems Based on Penalty Function Method. Comput. Mech. 2011, 48, 541–550. [Google Scholar] [CrossRef]
- Ma, J.; Chen, G.; Ji, L.; Qian, L.; Dong, S. A General Methodology to Establish the Contact Force Model for Complex Contacting Surfaces. Mech. Syst. Signal Process. 2020, 140, 106700. [Google Scholar] [CrossRef]
- Ha, J.-S.; Hong, J.-W.; Kim, J.-W.; Han, S.-B.; Choi, C.-Y.; Song, H.-J.; Jang, J.-S.; Kim, D.-Y.; Ko, D.-C.; Yi, S.-H.; et al. The Effect of Boron (B) and Copper (Cu) on the Microstructure and Graphite Morphology of Spheroidal Graphite Cast Iron. Materials 2023, 16, 4225. [Google Scholar] [CrossRef]
- KS B 0801; Test Pieces for Tensile Test for Metallic Materials. Korean Standards Association: Seoul, Republic of Korea, 2007.
- Resapu, R.R.; Perumahanthi, L.R. Numerical Study of Bilinear Isotropic & Kinematic Elastic–Plastic Response under Cyclic Loading. Mater. Today Proc. 2021, 39, 1647–1654. [Google Scholar]
- ASTM D5276-19; Standard Test Method for Drop Test of Loaded Containers by Free Fall. ASTM International: West Conshohocken, PA, USA, 2019. [CrossRef]
- Korean Ministry of Government Legislation. Article 45 of the Regulations on Packaging and Transport of Radioactive Materials. National Law Information Center. 2023. Available online: https://www.law.go.kr/ (accessed on 17 August 2024).
- Unger, D.J. Generalized Tresca Yield Condition as a Family of Elliptic Curves with Application to Mode I Crack Problems. Z. Angew. Math. Phys. 2022, 73, 5. [Google Scholar] [CrossRef]
- Zhang, S.H.; Jiang, X.R. Proposal and Application of a New Yield Criterion for Metal Plastic Deformation. Arch. Appl. Mech. 2020, 90, 2243–2255. [Google Scholar] [CrossRef]
- Afrousheh, M.; Marzbanrad, J.; Göhlich, D. Topology Optimization of Energy Absorbers under Crashworthiness Using Modified Hybrid Cellular Automata (MHCA) Algorithm. Struct. Multidiscip. Optim. 2019, 60, 1021–1034. [Google Scholar] [CrossRef]
- Eschenauer, H.A.; Olhoff, N. Topology Optimization of Continuum Structures: A Review. Appl. Mech. Rev. 2001, 54, 331–390. [Google Scholar] [CrossRef]
- Hwang, J.-S.; Kim, S.-J.; Sung, C.-H. Study on the Optimal Design of Column Rib Structure of Horizontal Machine Tool Using Topology Optimization Technique. J. Korean Soc. Manuf. Technol. Eng. 2023, 32, 1–7. [Google Scholar]
- Kristiansen, H.; Poulios, K.; Aage, N. Topology Optimization of Structures in Transient Impacts with Coulomb Friction. Int. J. Numer. Methods Eng. 2021, 122, 5053–5075. [Google Scholar] [CrossRef]
- Han, J.; Furuta, K.; Kondoh, T.; Nishiwaki, S.; Terada, K. Topology Optimization of Finite Strain Elastoplastic Materials Using Continuous Adjoint Method: Formulation, Implementation, and Applications. Comput. Methods Appl. Mech. Eng. 2024, 429, 1–30. [Google Scholar] [CrossRef]
- Gupta, Y.; Iyer, R.; Dommeti, V.K.; Nutu, E.; Rana, M.; Merdji, A.; Biswas, J.K.; Roy, S. Design of Dental Implant Using Design of Experiment and Topology Optimization: A Finite Element Analysis Study. Proc. Inst. Mech. Eng. H 2021, 235, 157–166. [Google Scholar] [CrossRef]
- Zhu, J.; Cai, X.; Ma, D.; Zhang, J.; Ni, X. Improved Structural Design of Wind Turbine Blade Based on Topology and Size Optimization. Int. J. Low-Carbon Technol. 2022, 17, 69–79. [Google Scholar] [CrossRef]
- Xia, L.; Breitkopf, P. Recent Advances on Topology Optimization of Multiscale Nonlinear Structures. Arch. Comput. Methods Eng. 2017, 24, 227–249. [Google Scholar] [CrossRef]
- Jeong, M.H.; Kim, Y.I.; Park, K.J. Nonlinear Dynamic Response Structural Integrating the Body-in-White and Battery Pack of an Electric Vehicle Considering a Side Pole Impact Test. Trans. KSAE 2021, 29, 683–691. [Google Scholar] [CrossRef]
- Jo, J.H.; Lee, J.S. Simultaneous Topology Optimization Using Adaptive Weighting Factor for Additive Manufacturing of Statically Loaded Structures. Trans. Korean Soc. Mech. Eng. A 2021, 45, 715–726. [Google Scholar] [CrossRef]
- Wallin, M.; Tortorelli, D.A. Nonlinear Homogenization for Topology Optimization. Mech. Mater. 2020, 145, 1–11. [Google Scholar] [CrossRef]
Type | Packaging Container Volume (m3) |
---|---|
Circle | 0.263 |
Square | 0.334 |
Poisson’s Ratio | Young’s Modulus | Yield Strength | Ultimate Tensile Strength | Tangent Modulus |
---|---|---|---|---|
0.4 | 227 GPa | 385 MPa | 484 MPa | 1.83 GPa |
Case 1 | Corner 1 | Side 1 | Corner 2 | Side 2 | |
---|---|---|---|---|---|
Total maximum Tresca stress (MPa) | 511.42 | 1468.1 | 823.42 | 1094.8 | 507.01 |
Inner maximum Tresca stress (MPa) | 221.58 | 1073.9 | 252.45 | 602.43 | 254.61 |
Need for reinforcement | - | O | O | O | O |
Reference | Optimization Model | Analysis Condition | Optimization Method | Note |
---|---|---|---|---|
Kim [6] | Rod Truss, Cantilever Plate, Cylindrical Tube Structure, Joined-Wing | Nonlinear dynamic analysis Equivalent static loads | Structural optimization | - |
Jeong [4] | Vehicle frontal structures | Nonlinear dynamic analysis Equivalent static loads | Structural optimization Topology optimization | - |
Yi Rong [8] | Support structure, arch bridge, table, hinge arm, and MBB beam | Static loads | Topology optimization | Adaptive design domain |
Jie Zhu [25] | Wind turbine blades | Static loads | Topology optimization | Multiple weighting factors |
Liang Xia [26] | Cantilever | Static loads | Topology optimization | Multi-scale |
Corner 1 | Side 1 | Corner 2 | Side 2 | |
---|---|---|---|---|
Equivalent plastic strain (Model 1) | 0.688 | 0.047 | 0.217 | 0.048 |
Average Tresca stress (Model 2) | 0.178 | 0.372 | 0.172 | 0.279 |
Plastic work (Model 3) | 0.266 | 0.271 | 0.259 | 0.204 |
Initial Model | Equivalent Plastic Strain (Model 1) | Average Tresca Stress Factor (Model 2) | Plastic Work (Model 3) | |
---|---|---|---|---|
Optimized volume (%) | - | 4.83 | 4.86 | 4.83 |
Loadable volume (106 mm3) | 305.88 | 301.59 | 300.98 | 301.58 |
Loadable volume (%) | Standard | −1.4 | −1.6 | −1.4 |
Internal Tresca Stress (MPa) | ||||
---|---|---|---|---|
Corner 1 | Side 1 | Corner 2 | Side 2 | |
Equivalent plastic strain (Model 1) | 216.02 | 221.92 | 208.58 | 256.88 |
Average Tresca stress (Model 2) | 177.64 | 219.75 | 212.38 | 226.66 |
Plastic work (Model 3) | 217.72 | 220.95 | 202.56 | 234.99 |
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Lee, J.-I.; Park, S.-W.; Song, H.-J.; Cho, Y.-J.; Kim, D.-H.; Ko, D.-C.; Jang, J.-S. Multi-Load Topology Optimization Design for the Structural Safety Maintenance of Low- and Intermediate-Level Radioactive Waste Packaging Containers in the Case of a Collision. Materials 2024, 17, 4130. https://doi.org/10.3390/ma17164130
Lee J-I, Park S-W, Song H-J, Cho Y-J, Kim D-H, Ko D-C, Jang J-S. Multi-Load Topology Optimization Design for the Structural Safety Maintenance of Low- and Intermediate-Level Radioactive Waste Packaging Containers in the Case of a Collision. Materials. 2024; 17(16):4130. https://doi.org/10.3390/ma17164130
Chicago/Turabian StyleLee, Jeong-In, Sang-Wook Park, Hye-Jin Song, Yong-Jae Cho, Dong-Hwan Kim, Dae-Cheol Ko, and Jin-Seok Jang. 2024. "Multi-Load Topology Optimization Design for the Structural Safety Maintenance of Low- and Intermediate-Level Radioactive Waste Packaging Containers in the Case of a Collision" Materials 17, no. 16: 4130. https://doi.org/10.3390/ma17164130