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Bounds for decoupled design and analysis discretizations in topology optimization
Summary Topology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution. This paper discusses the relation between the number of design variables per element and the order of the elements used for analysis. We derive that beyo...
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| Published in: | International journal for numerical methods in engineering 2017-07, Vol.111 (1), p.88-100 |
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| Main Authors: | , , , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c3275-98308f8446bc69c13cbef9d2af7e7b45e1624b058d85e1e66d10277e6f86ad1f3 |
| container_end_page | 100 |
| container_issue | 1 |
| container_start_page | 88 |
| container_title | International journal for numerical methods in engineering |
| container_volume | 111 |
| creator | Gupta, D. K. van der Veen, G. J. Aragón, A. M. Langelaar, M. van Keulen, F. |
| description | Summary
Topology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution. This paper discusses the relation between the number of design variables per element and the order of the elements used for analysis. We derive that beyond a maximum number of design variables, certain sets of material distributions cannot be discriminated based on the corresponding analysis results. This makes the design description inefficient and the solution of the optimization problem non‐unique. To prevent this, we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing non‐uniqueness. Copyright © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd. |
| doi_str_mv | 10.1002/nme.5455 |
| format | article |
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Topology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution. This paper discusses the relation between the number of design variables per element and the order of the elements used for analysis. We derive that beyond a maximum number of design variables, certain sets of material distributions cannot be discriminated based on the corresponding analysis results. This makes the design description inefficient and the solution of the optimization problem non‐unique. To prevent this, we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing non‐uniqueness. Copyright © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd.</description><identifier>ISSN: 0029-5981</identifier><identifier>EISSN: 1097-0207</identifier><identifier>DOI: 10.1002/nme.5455</identifier><language>eng</language><publisher>Chichester, UK: John Wiley & Sons, Ltd</publisher><subject>Copyright ; Design analysis ; Design engineering ; Design improvements ; Design optimization ; Discretization ; Finite element method ; finite element methods ; Formulations ; Numerical methods ; structures ; topology design ; Topology optimization ; Uniqueness</subject><ispartof>International journal for numerical methods in engineering, 2017-07, Vol.111 (1), p.88-100</ispartof><rights>Copyright © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd</rights><rights>Copyright © 2017 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3275-98308f8446bc69c13cbef9d2af7e7b45e1624b058d85e1e66d10277e6f86ad1f3</citedby><cites>FETCH-LOGICAL-c3275-98308f8446bc69c13cbef9d2af7e7b45e1624b058d85e1e66d10277e6f86ad1f3</cites><orcidid>0000-0003-2275-6207</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Gupta, D. K.</creatorcontrib><creatorcontrib>van der Veen, G. J.</creatorcontrib><creatorcontrib>Aragón, A. M.</creatorcontrib><creatorcontrib>Langelaar, M.</creatorcontrib><creatorcontrib>van Keulen, F.</creatorcontrib><title>Bounds for decoupled design and analysis discretizations in topology optimization</title><title>International journal for numerical methods in engineering</title><description>Summary
Topology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution. This paper discusses the relation between the number of design variables per element and the order of the elements used for analysis. We derive that beyond a maximum number of design variables, certain sets of material distributions cannot be discriminated based on the corresponding analysis results. This makes the design description inefficient and the solution of the optimization problem non‐unique. To prevent this, we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing non‐uniqueness. Copyright © 2016 The Authors. 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Topology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution. This paper discusses the relation between the number of design variables per element and the order of the elements used for analysis. We derive that beyond a maximum number of design variables, certain sets of material distributions cannot be discriminated based on the corresponding analysis results. This makes the design description inefficient and the solution of the optimization problem non‐unique. To prevent this, we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing non‐uniqueness. Copyright © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd.</abstract><cop>Chichester, UK</cop><pub>John Wiley & Sons, Ltd</pub><doi>10.1002/nme.5455</doi><tpages>13</tpages><orcidid>https://orcid.org/0000-0003-2275-6207</orcidid><oa>free_for_read</oa></addata></record> |
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| identifier | ISSN: 0029-5981 |
| ispartof | International journal for numerical methods in engineering, 2017-07, Vol.111 (1), p.88-100 |
| issn | 0029-5981 1097-0207 |
| language | eng |
| recordid | cdi_proquest_journals_1905652066 |
| source | Wiley-Blackwell Read & Publish Collection |
| subjects | Copyright Design analysis Design engineering Design improvements Design optimization Discretization Finite element method finite element methods Formulations Numerical methods structures topology design Topology optimization Uniqueness |
| title | Bounds for decoupled design and analysis discretizations in topology optimization |
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