Some considerations on multi-material topology optimization using ordered SIMP

Abstract Ordered solid isotropic material with penalization (SIMP) interpolation has emerged as an interesting technique in multi-material topology optimization. The computational cost of this approach is independent of the number of materials considered. However, an unusual behavior is observed whe...
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Autor*in:	da Silveira, Otavio Augusto Alves [verfasserIn] Palma, Lucas Farias

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Topology optimization Multi-material Ordered SIMP Material model

Anmerkung:	© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Übergeordnetes Werk:	Enthalten in: Structural and multidisciplinary optimization - Berlin : Springer, 1989, 65(2022), 9 vom: Sept.
Übergeordnetes Werk:	volume:65 ; year:2022 ; number:9 ; month:09

Links:	Volltext

DOI / URN:	10.1007/s00158-022-03379-7

Katalog-ID:	SPR048025232

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520			\|a Abstract Ordered solid isotropic material with penalization (SIMP) interpolation has emerged as an interesting technique in multi-material topology optimization. The computational cost of this approach is independent of the number of materials considered. However, an unusual behavior is observed when using the original material model equations (Zuo and Saitou in Struct Multidisc Optim 55:477–491, 2017). This paper proposes modified material and cost models for ordered interpolation. This new ordered SIMP presents the desired interpolation characteristics discussed in the original paper and is suitable for non-monotonic properties. Density filtering is used to remove checkerboard patterns and ensure mesh convergence. A threshold projection is tailored for multi-material ordered SIMP in order to reduce the presence of intermediate densities. A comparative analysis of the original interpolation with the modified one is made through various numerical examples. Some issues related to the filtering techniques and boundary effects on an ordered SIMP are identified.
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allfields	10.1007/s00158-022-03379-7 doi (DE-627)SPR048025232 (SPR)s00158-022-03379-7-e DE-627 ger DE-627 rakwb eng da Silveira, Otavio Augusto Alves verfasserin (orcid)0000-0002-7184-5479 aut Some considerations on multi-material topology optimization using ordered SIMP 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Ordered solid isotropic material with penalization (SIMP) interpolation has emerged as an interesting technique in multi-material topology optimization. The computational cost of this approach is independent of the number of materials considered. However, an unusual behavior is observed when using the original material model equations (Zuo and Saitou in Struct Multidisc Optim 55:477–491, 2017). This paper proposes modified material and cost models for ordered interpolation. This new ordered SIMP presents the desired interpolation characteristics discussed in the original paper and is suitable for non-monotonic properties. Density filtering is used to remove checkerboard patterns and ensure mesh convergence. A threshold projection is tailored for multi-material ordered SIMP in order to reduce the presence of intermediate densities. A comparative analysis of the original interpolation with the modified one is made through various numerical examples. Some issues related to the filtering techniques and boundary effects on an ordered SIMP are identified. Topology optimization (dpeaa)DE-He213 Multi-material (dpeaa)DE-He213 Ordered SIMP (dpeaa)DE-He213 Material model (dpeaa)DE-He213 Palma, Lucas Farias aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 65(2022), 9 vom: Sept. (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:65 year:2022 number:9 month:09 https://dx.doi.org/10.1007/s00158-022-03379-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 65 2022 9 09
spelling	10.1007/s00158-022-03379-7 doi (DE-627)SPR048025232 (SPR)s00158-022-03379-7-e DE-627 ger DE-627 rakwb eng da Silveira, Otavio Augusto Alves verfasserin (orcid)0000-0002-7184-5479 aut Some considerations on multi-material topology optimization using ordered SIMP 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Ordered solid isotropic material with penalization (SIMP) interpolation has emerged as an interesting technique in multi-material topology optimization. The computational cost of this approach is independent of the number of materials considered. However, an unusual behavior is observed when using the original material model equations (Zuo and Saitou in Struct Multidisc Optim 55:477–491, 2017). This paper proposes modified material and cost models for ordered interpolation. This new ordered SIMP presents the desired interpolation characteristics discussed in the original paper and is suitable for non-monotonic properties. Density filtering is used to remove checkerboard patterns and ensure mesh convergence. A threshold projection is tailored for multi-material ordered SIMP in order to reduce the presence of intermediate densities. A comparative analysis of the original interpolation with the modified one is made through various numerical examples. Some issues related to the filtering techniques and boundary effects on an ordered SIMP are identified. Topology optimization (dpeaa)DE-He213 Multi-material (dpeaa)DE-He213 Ordered SIMP (dpeaa)DE-He213 Material model (dpeaa)DE-He213 Palma, Lucas Farias aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 65(2022), 9 vom: Sept. (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:65 year:2022 number:9 month:09 https://dx.doi.org/10.1007/s00158-022-03379-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 65 2022 9 09
allfields_unstemmed	10.1007/s00158-022-03379-7 doi (DE-627)SPR048025232 (SPR)s00158-022-03379-7-e DE-627 ger DE-627 rakwb eng da Silveira, Otavio Augusto Alves verfasserin (orcid)0000-0002-7184-5479 aut Some considerations on multi-material topology optimization using ordered SIMP 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Ordered solid isotropic material with penalization (SIMP) interpolation has emerged as an interesting technique in multi-material topology optimization. The computational cost of this approach is independent of the number of materials considered. However, an unusual behavior is observed when using the original material model equations (Zuo and Saitou in Struct Multidisc Optim 55:477–491, 2017). This paper proposes modified material and cost models for ordered interpolation. This new ordered SIMP presents the desired interpolation characteristics discussed in the original paper and is suitable for non-monotonic properties. Density filtering is used to remove checkerboard patterns and ensure mesh convergence. A threshold projection is tailored for multi-material ordered SIMP in order to reduce the presence of intermediate densities. A comparative analysis of the original interpolation with the modified one is made through various numerical examples. Some issues related to the filtering techniques and boundary effects on an ordered SIMP are identified. Topology optimization (dpeaa)DE-He213 Multi-material (dpeaa)DE-He213 Ordered SIMP (dpeaa)DE-He213 Material model (dpeaa)DE-He213 Palma, Lucas Farias aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 65(2022), 9 vom: Sept. (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:65 year:2022 number:9 month:09 https://dx.doi.org/10.1007/s00158-022-03379-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 65 2022 9 09
allfieldsGer	10.1007/s00158-022-03379-7 doi (DE-627)SPR048025232 (SPR)s00158-022-03379-7-e DE-627 ger DE-627 rakwb eng da Silveira, Otavio Augusto Alves verfasserin (orcid)0000-0002-7184-5479 aut Some considerations on multi-material topology optimization using ordered SIMP 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Ordered solid isotropic material with penalization (SIMP) interpolation has emerged as an interesting technique in multi-material topology optimization. The computational cost of this approach is independent of the number of materials considered. However, an unusual behavior is observed when using the original material model equations (Zuo and Saitou in Struct Multidisc Optim 55:477–491, 2017). This paper proposes modified material and cost models for ordered interpolation. This new ordered SIMP presents the desired interpolation characteristics discussed in the original paper and is suitable for non-monotonic properties. Density filtering is used to remove checkerboard patterns and ensure mesh convergence. A threshold projection is tailored for multi-material ordered SIMP in order to reduce the presence of intermediate densities. A comparative analysis of the original interpolation with the modified one is made through various numerical examples. Some issues related to the filtering techniques and boundary effects on an ordered SIMP are identified. Topology optimization (dpeaa)DE-He213 Multi-material (dpeaa)DE-He213 Ordered SIMP (dpeaa)DE-He213 Material model (dpeaa)DE-He213 Palma, Lucas Farias aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 65(2022), 9 vom: Sept. (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:65 year:2022 number:9 month:09 https://dx.doi.org/10.1007/s00158-022-03379-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 65 2022 9 09
allfieldsSound	10.1007/s00158-022-03379-7 doi (DE-627)SPR048025232 (SPR)s00158-022-03379-7-e DE-627 ger DE-627 rakwb eng da Silveira, Otavio Augusto Alves verfasserin (orcid)0000-0002-7184-5479 aut Some considerations on multi-material topology optimization using ordered SIMP 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Ordered solid isotropic material with penalization (SIMP) interpolation has emerged as an interesting technique in multi-material topology optimization. The computational cost of this approach is independent of the number of materials considered. However, an unusual behavior is observed when using the original material model equations (Zuo and Saitou in Struct Multidisc Optim 55:477–491, 2017). This paper proposes modified material and cost models for ordered interpolation. This new ordered SIMP presents the desired interpolation characteristics discussed in the original paper and is suitable for non-monotonic properties. Density filtering is used to remove checkerboard patterns and ensure mesh convergence. A threshold projection is tailored for multi-material ordered SIMP in order to reduce the presence of intermediate densities. A comparative analysis of the original interpolation with the modified one is made through various numerical examples. Some issues related to the filtering techniques and boundary effects on an ordered SIMP are identified. Topology optimization (dpeaa)DE-He213 Multi-material (dpeaa)DE-He213 Ordered SIMP (dpeaa)DE-He213 Material model (dpeaa)DE-He213 Palma, Lucas Farias aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 65(2022), 9 vom: Sept. (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:65 year:2022 number:9 month:09 https://dx.doi.org/10.1007/s00158-022-03379-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 65 2022 9 09
language	English
source	Enthalten in Structural and multidisciplinary optimization 65(2022), 9 vom: Sept. volume:65 year:2022 number:9 month:09
sourceStr	Enthalten in Structural and multidisciplinary optimization 65(2022), 9 vom: Sept. volume:65 year:2022 number:9 month:09
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Topology optimization Multi-material Ordered SIMP Material model
isfreeaccess_bool	false
container_title	Structural and multidisciplinary optimization
authorswithroles_txt_mv	da Silveira, Otavio Augusto Alves @@aut@@ Palma, Lucas Farias @@aut@@
publishDateDaySort_date	2022-09-01T00:00:00Z
hierarchy_top_id	271602503
id	SPR048025232
language_de	englisch
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author	da Silveira, Otavio Augusto Alves
spellingShingle	da Silveira, Otavio Augusto Alves misc Topology optimization misc Multi-material misc Ordered SIMP misc Material model Some considerations on multi-material topology optimization using ordered SIMP
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topic_title	Some considerations on multi-material topology optimization using ordered SIMP Topology optimization (dpeaa)DE-He213 Multi-material (dpeaa)DE-He213 Ordered SIMP (dpeaa)DE-He213 Material model (dpeaa)DE-He213
topic	misc Topology optimization misc Multi-material misc Ordered SIMP misc Material model
topic_unstemmed	misc Topology optimization misc Multi-material misc Ordered SIMP misc Material model
topic_browse	misc Topology optimization misc Multi-material misc Ordered SIMP misc Material model
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title	Some considerations on multi-material topology optimization using ordered SIMP
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title_full	Some considerations on multi-material topology optimization using ordered SIMP
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title_sort	some considerations on multi-material topology optimization using ordered simp
title_auth	Some considerations on multi-material topology optimization using ordered SIMP
abstract	Abstract Ordered solid isotropic material with penalization (SIMP) interpolation has emerged as an interesting technique in multi-material topology optimization. The computational cost of this approach is independent of the number of materials considered. However, an unusual behavior is observed when using the original material model equations (Zuo and Saitou in Struct Multidisc Optim 55:477–491, 2017). This paper proposes modified material and cost models for ordered interpolation. This new ordered SIMP presents the desired interpolation characteristics discussed in the original paper and is suitable for non-monotonic properties. Density filtering is used to remove checkerboard patterns and ensure mesh convergence. A threshold projection is tailored for multi-material ordered SIMP in order to reduce the presence of intermediate densities. A comparative analysis of the original interpolation with the modified one is made through various numerical examples. Some issues related to the filtering techniques and boundary effects on an ordered SIMP are identified. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstractGer	Abstract Ordered solid isotropic material with penalization (SIMP) interpolation has emerged as an interesting technique in multi-material topology optimization. The computational cost of this approach is independent of the number of materials considered. However, an unusual behavior is observed when using the original material model equations (Zuo and Saitou in Struct Multidisc Optim 55:477–491, 2017). This paper proposes modified material and cost models for ordered interpolation. This new ordered SIMP presents the desired interpolation characteristics discussed in the original paper and is suitable for non-monotonic properties. Density filtering is used to remove checkerboard patterns and ensure mesh convergence. A threshold projection is tailored for multi-material ordered SIMP in order to reduce the presence of intermediate densities. A comparative analysis of the original interpolation with the modified one is made through various numerical examples. Some issues related to the filtering techniques and boundary effects on an ordered SIMP are identified. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstract_unstemmed	Abstract Ordered solid isotropic material with penalization (SIMP) interpolation has emerged as an interesting technique in multi-material topology optimization. The computational cost of this approach is independent of the number of materials considered. However, an unusual behavior is observed when using the original material model equations (Zuo and Saitou in Struct Multidisc Optim 55:477–491, 2017). This paper proposes modified material and cost models for ordered interpolation. This new ordered SIMP presents the desired interpolation characteristics discussed in the original paper and is suitable for non-monotonic properties. Density filtering is used to remove checkerboard patterns and ensure mesh convergence. A threshold projection is tailored for multi-material ordered SIMP in order to reduce the presence of intermediate densities. A comparative analysis of the original interpolation with the modified one is made through various numerical examples. Some issues related to the filtering techniques and boundary effects on an ordered SIMP are identified. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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title_short	Some considerations on multi-material topology optimization using ordered SIMP
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up_date	2024-07-03T16:31:02.339Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR048025232</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230509112152.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">220908s2022 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00158-022-03379-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR048025232</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00158-022-03379-7-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">da Silveira, Otavio Augusto Alves</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0002-7184-5479</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Some considerations on multi-material topology optimization using ordered SIMP</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Ordered solid isotropic material with penalization (SIMP) interpolation has emerged as an interesting technique in multi-material topology optimization. The computational cost of this approach is independent of the number of materials considered. However, an unusual behavior is observed when using the original material model equations (Zuo and Saitou in Struct Multidisc Optim 55:477–491, 2017). This paper proposes modified material and cost models for ordered interpolation. This new ordered SIMP presents the desired interpolation characteristics discussed in the original paper and is suitable for non-monotonic properties. Density filtering is used to remove checkerboard patterns and ensure mesh convergence. A threshold projection is tailored for multi-material ordered SIMP in order to reduce the presence of intermediate densities. A comparative analysis of the original interpolation with the modified one is made through various numerical examples. 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