A Reconstruction Approach for Concurrent Multiscale Topology Optimization Based on Direct FE<sup>2</sup> Method
The rapid development of material science is increasing the demand for the multiscale design of materials. The concurrent multiscale topology optimization based on the Direct FE<sup>2</sup> method can greatly improve computational efficiency, but it may lead to the checkerboard problem....
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| Format: | Article |
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/12/2779 |
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| author | Ang Zhao Vincent Beng Chye Tan Pei Li Kui Liu Zhendong Hu |
| author_facet | Ang Zhao Vincent Beng Chye Tan Pei Li Kui Liu Zhendong Hu |
| author_sort | Ang Zhao |
| collection | DOAJ |
| description | The rapid development of material science is increasing the demand for the multiscale design of materials. The concurrent multiscale topology optimization based on the Direct FE<sup>2</sup> method can greatly improve computational efficiency, but it may lead to the checkerboard problem. In order to solve the checkerboard problem and reconstruct the results of the Direct FE<sup>2</sup> model, this paper proposes a filtering-based reconstruction method. This solution is of great significance for the practical application of multiscale topology optimization, as it not only solves the checkerboard problem but also provides the optimized full model based on interpolation. The filtering method effectively eliminates the checkerboard pattern in the results by smoothing the element densities. The reconstruction method restores the smoothness of the optimized structure by interpolating between the filtered densities. This method is highly effective in solving the checkerboard problem, as demonstrated in our numerical examples. The results show that the proposed algorithm produces feasible and stable results. |
| first_indexed | 2024-03-11T02:11:30Z |
| format | Article |
| id | doaj.art-951af62eaf754eb68c27d2f23144a963 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T02:11:30Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-951af62eaf754eb68c27d2f23144a9632023-11-18T11:29:41ZengMDPI AGMathematics2227-73902023-06-011112277910.3390/math11122779A Reconstruction Approach for Concurrent Multiscale Topology Optimization Based on Direct FE<sup>2</sup> MethodAng Zhao0Vincent Beng Chye Tan1Pei Li2Kui Liu3Zhendong Hu4School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, ChinaDepartment of Mechanical Engineering, National University of Singapore, Singapore 119260, SingaporeInternational Machinery Center, Department of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, ChinaShanghai Aerospace Control Technology Institute, Shanghai 201109, ChinaSchool of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, ChinaThe rapid development of material science is increasing the demand for the multiscale design of materials. The concurrent multiscale topology optimization based on the Direct FE<sup>2</sup> method can greatly improve computational efficiency, but it may lead to the checkerboard problem. In order to solve the checkerboard problem and reconstruct the results of the Direct FE<sup>2</sup> model, this paper proposes a filtering-based reconstruction method. This solution is of great significance for the practical application of multiscale topology optimization, as it not only solves the checkerboard problem but also provides the optimized full model based on interpolation. The filtering method effectively eliminates the checkerboard pattern in the results by smoothing the element densities. The reconstruction method restores the smoothness of the optimized structure by interpolating between the filtered densities. This method is highly effective in solving the checkerboard problem, as demonstrated in our numerical examples. The results show that the proposed algorithm produces feasible and stable results.https://www.mdpi.com/2227-7390/11/12/2779topology optimizationmultiscale analysisdirect FE<sup>2</sup>reconstructionfilter |
| spellingShingle | Ang Zhao Vincent Beng Chye Tan Pei Li Kui Liu Zhendong Hu A Reconstruction Approach for Concurrent Multiscale Topology Optimization Based on Direct FE<sup>2</sup> Method Mathematics topology optimization multiscale analysis direct FE<sup>2</sup> reconstruction filter |
| title | A Reconstruction Approach for Concurrent Multiscale Topology Optimization Based on Direct FE<sup>2</sup> Method |
| title_full | A Reconstruction Approach for Concurrent Multiscale Topology Optimization Based on Direct FE<sup>2</sup> Method |
| title_fullStr | A Reconstruction Approach for Concurrent Multiscale Topology Optimization Based on Direct FE<sup>2</sup> Method |
| title_full_unstemmed | A Reconstruction Approach for Concurrent Multiscale Topology Optimization Based on Direct FE<sup>2</sup> Method |
| title_short | A Reconstruction Approach for Concurrent Multiscale Topology Optimization Based on Direct FE<sup>2</sup> Method |
| title_sort | reconstruction approach for concurrent multiscale topology optimization based on direct fe sup 2 sup method |
| topic | topology optimization multiscale analysis direct FE<sup>2</sup> reconstruction filter |
| url | https://www.mdpi.com/2227-7390/11/12/2779 |
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