A Hybrid Level Set Method for the Topology Optimization of Functionally Graded Structures
This paper presents a hybrid level set method (HLSM) to design novelty functionally graded structures (FGSs) with complex macroscopic graded patterns. The hybrid level set function (HLSF) is constructed to parametrically model the macro unit cells by introducing the affine concept of convex optimiza...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-06-01
|
| Series: | Materials |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1996-1944/15/13/4483 |
| _version_ | 1797408721177935872 |
|---|---|
| author | Junjian Fu Zhengtao Shu Liang Gao Xiangman Zhou |
| author_facet | Junjian Fu Zhengtao Shu Liang Gao Xiangman Zhou |
| author_sort | Junjian Fu |
| collection | DOAJ |
| description | This paper presents a hybrid level set method (HLSM) to design novelty functionally graded structures (FGSs) with complex macroscopic graded patterns. The hybrid level set function (HLSF) is constructed to parametrically model the macro unit cells by introducing the affine concept of convex optimization theory. The global weight coefficients on macro unit cell nodes and the local weight coefficients within the macro unit cell are defined as master and slave design variables, respectively. The local design variables are interpolated by the global design variables to guarantee the C<sup>0</sup> continuity of neighboring unit cells. A HLSM-based topology optimization model for the FGSs is established to maximize structural stiffness. The optimization model is solved by the optimality criteria (OC) algorithm. Two typical FGSs design problems are investigated, including thin-walled stiffened structures (TWSSs) and functionally graded cellular structures (FGCSs). In addition, additively manufactured FGCSs with different core layers are tested for bending performance. Numerical examples show that the HLSM is effective for designing FGSs like TWSSs and FGCSs. The bending tests prove that FGSs designed using HLSM are have a high performance. |
| first_indexed | 2024-03-09T04:03:41Z |
| format | Article |
| id | doaj.art-813258fee8fa4cd9bc22218a5aab0fc7 |
| institution | Directory Open Access Journal |
| issn | 1996-1944 |
| language | English |
| last_indexed | 2024-03-09T04:03:41Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Materials |
| spelling | doaj.art-813258fee8fa4cd9bc22218a5aab0fc72023-12-03T14:10:01ZengMDPI AGMaterials1996-19442022-06-011513448310.3390/ma15134483A Hybrid Level Set Method for the Topology Optimization of Functionally Graded StructuresJunjian Fu0Zhengtao Shu1Liang Gao2Xiangman Zhou3Hubei Key Laboratory of Hydroelectric Machinery Design & Maintenance, Yichang 443002, ChinaCollege of Mechanical and Power Engineering, China Three Gorges University, Yichang 443002, ChinaState Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, ChinaHubei Key Laboratory of Hydroelectric Machinery Design & Maintenance, Yichang 443002, ChinaThis paper presents a hybrid level set method (HLSM) to design novelty functionally graded structures (FGSs) with complex macroscopic graded patterns. The hybrid level set function (HLSF) is constructed to parametrically model the macro unit cells by introducing the affine concept of convex optimization theory. The global weight coefficients on macro unit cell nodes and the local weight coefficients within the macro unit cell are defined as master and slave design variables, respectively. The local design variables are interpolated by the global design variables to guarantee the C<sup>0</sup> continuity of neighboring unit cells. A HLSM-based topology optimization model for the FGSs is established to maximize structural stiffness. The optimization model is solved by the optimality criteria (OC) algorithm. Two typical FGSs design problems are investigated, including thin-walled stiffened structures (TWSSs) and functionally graded cellular structures (FGCSs). In addition, additively manufactured FGCSs with different core layers are tested for bending performance. Numerical examples show that the HLSM is effective for designing FGSs like TWSSs and FGCSs. The bending tests prove that FGSs designed using HLSM are have a high performance.https://www.mdpi.com/1996-1944/15/13/4483topology optimizationhybrid level set methodthin-walled stiffened structuresfunctionally graded cellular structures |
| spellingShingle | Junjian Fu Zhengtao Shu Liang Gao Xiangman Zhou A Hybrid Level Set Method for the Topology Optimization of Functionally Graded Structures Materials topology optimization hybrid level set method thin-walled stiffened structures functionally graded cellular structures |
| title | A Hybrid Level Set Method for the Topology Optimization of Functionally Graded Structures |
| title_full | A Hybrid Level Set Method for the Topology Optimization of Functionally Graded Structures |
| title_fullStr | A Hybrid Level Set Method for the Topology Optimization of Functionally Graded Structures |
| title_full_unstemmed | A Hybrid Level Set Method for the Topology Optimization of Functionally Graded Structures |
| title_short | A Hybrid Level Set Method for the Topology Optimization of Functionally Graded Structures |
| title_sort | hybrid level set method for the topology optimization of functionally graded structures |
| topic | topology optimization hybrid level set method thin-walled stiffened structures functionally graded cellular structures |
| url | https://www.mdpi.com/1996-1944/15/13/4483 |
| work_keys_str_mv | AT junjianfu ahybridlevelsetmethodforthetopologyoptimizationoffunctionallygradedstructures AT zhengtaoshu ahybridlevelsetmethodforthetopologyoptimizationoffunctionallygradedstructures AT lianggao ahybridlevelsetmethodforthetopologyoptimizationoffunctionallygradedstructures AT xiangmanzhou ahybridlevelsetmethodforthetopologyoptimizationoffunctionallygradedstructures AT junjianfu hybridlevelsetmethodforthetopologyoptimizationoffunctionallygradedstructures AT zhengtaoshu hybridlevelsetmethodforthetopologyoptimizationoffunctionallygradedstructures AT lianggao hybridlevelsetmethodforthetopologyoptimizationoffunctionallygradedstructures AT xiangmanzhou hybridlevelsetmethodforthetopologyoptimizationoffunctionallygradedstructures |