Topology optimization under design-dependent loads with the parameterized level-set method based on radial-basis functions
Based on the parameterized level-set method using radial basis functions, a topology optimization method is proposed that can account for design-dependent loads. First, a mathematical model of the optimization problem is established with the structural compliance minimization as the objective functi...
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| Veröffentlicht in: | Computer methods in applied mechanics and engineering Jg. 369; S. 113235 |
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| Sprache: | Englisch |
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01.09.2020
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| ISSN: | 0045-7825, 1879-2138 |
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| Abstract | Based on the parameterized level-set method using radial basis functions, a topology optimization method is proposed that can account for design-dependent loads. First, a mathematical model of the optimization problem is established with the structural compliance minimization as the objective function and the structural volume fraction as the design constraint. By converting the line integrals into volume integrals, the design-dependent loads imposed on the structure outline described by the zero-level set are converted, and a relatively easy boundary detection method is used. Subsequently, an updating strategy of the Lagrange multiplier is proposed to make the transition of the objective function smooth during the convergence process. Finally, the effectiveness and efficiency of the proposed optimization method in solving design-dependent load problems can be shown through several classic numerical examples.
•Topology optimization is applied to design-dependent loads problem.•Radial basis functions and shape derivatives are used in parameterized level set method.•A new boundary detection method is presented.•A new update strategy of Lagrange multiplier is proposed. |
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| AbstractList | Based on the parameterized level-set method using radial basis functions, a topology optimization method is proposed that can account for design-dependent loads. First, a mathematical model of the optimization problem is established with the structural compliance minimization as the objective function and the structural volume fraction as the design constraint. By converting the line integrals into volume integrals, the design-dependent loads imposed on the structure outline described by the zero-level set are converted, and a relatively easy boundary detection method is used. Subsequently, an updating strategy of the Lagrange multiplier is proposed to make the transition of the objective function smooth during the convergence process. Finally, the effectiveness and efficiency of the proposed optimization method in solving design-dependent load problems can be shown through several classic numerical examples. Based on the parameterized level-set method using radial basis functions, a topology optimization method is proposed that can account for design-dependent loads. First, a mathematical model of the optimization problem is established with the structural compliance minimization as the objective function and the structural volume fraction as the design constraint. By converting the line integrals into volume integrals, the design-dependent loads imposed on the structure outline described by the zero-level set are converted, and a relatively easy boundary detection method is used. Subsequently, an updating strategy of the Lagrange multiplier is proposed to make the transition of the objective function smooth during the convergence process. Finally, the effectiveness and efficiency of the proposed optimization method in solving design-dependent load problems can be shown through several classic numerical examples. •Topology optimization is applied to design-dependent loads problem.•Radial basis functions and shape derivatives are used in parameterized level set method.•A new boundary detection method is presented.•A new update strategy of Lagrange multiplier is proposed. |
| ArticleNumber | 113235 |
| Author | Zhao, Min Jiang, Yuanteng |
| Author_xml | – sequence: 1 givenname: Yuanteng surname: Jiang fullname: Jiang, Yuanteng organization: State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China – sequence: 2 givenname: Min surname: Zhao fullname: Zhao, Min email: min.zhao@sjtu.edu.cn organization: State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China |
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| Cites_doi | 10.1016/j.cma.2012.04.007 10.1080/0305215X.2016.1164147 10.1016/0021-9991(88)90002-2 10.1016/j.cma.2014.09.022 10.1016/j.finel.2017.07.005 10.1007/s00158-019-02339-y 10.1007/s00158-004-0379-y 10.1007/s00158-008-0317-5 10.1007/s00158-013-0956-z 10.1006/jcph.2000.6581 10.1007/s001580050088 10.1016/0045-7949(95)00235-9 10.1016/S0045-7825(02)00559-5 10.1109/TIP.2010.2069690 10.1002/nme.5827 10.1007/BF01650949 10.1016/j.finel.2015.01.009 10.1007/s00158-018-1904-8 10.1016/j.finel.2015.07.010 10.1007/s00158-007-0221-4 10.1016/j.finel.2017.10.006 10.1007/BF01742754 10.1007/s00158-015-1376-z 10.1016/j.cma.2006.09.021 10.1002/nme.2092 10.1007/s001580050176 10.1016/j.jcp.2003.09.032 10.1016/j.jcp.2006.06.029 |
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| Keywords | Topology optimization Design-dependent load Radial basis functions Level-set method Boundary detection method |
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| SubjectTerms | Boundary detection method Design optimization Design-dependent load Integrals Lagrange multiplier Level-set method Loads (forces) Optimization Parameterization Radial basis function Radial basis functions Topology optimization |
| Title | Topology optimization under design-dependent loads with the parameterized level-set method based on radial-basis functions |
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