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Erschienen in: Structural and Multidisciplinary Optimization 6/2019

28.03.2019 | Research Paper

Configuration optimization for thin structures using level set method

verfasst von: Gang-Won Jang, Sandilya Kambampati, Hayoung Chung, H. Alicia Kim

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 6/2019

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Abstract

Level set–based optimization for two-dimensional structural configurations with thin members is presented. A structural domain with thin thickness is defined as a narrow band region on the zero-level contour of the level set function. No additional constraints or penalty functional is required to enforce semi-uniformity in member thickness. Design velocity is calculated on the zero level set, not on domain boundaries, and extended to level set grids in the narrow band. For complicated structural layouts, multiple level set functions are employed. The effectiveness of the proposed method is verified by solving optimization problems of bar configurations. Since no thickness constraints are employed, structurally unfavorable distorted joints seen in other literature do not appear in the results.

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Literatur
Zurück zum Zitat Adalsteinsson D, Sethian JA (1999) The fast construction of extension velocities in level set methods. J Comput Phys 148:2–22MathSciNetCrossRefMATH Adalsteinsson D, Sethian JA (1999) The fast construction of extension velocities in level set methods. J Comput Phys 148:2–22MathSciNetCrossRefMATH
Zurück zum Zitat Allaire G, Jouve F, Toader A-M (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1):363–393MathSciNetCrossRefMATH Allaire G, Jouve F, Toader A-M (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1):363–393MathSciNetCrossRefMATH
Zurück zum Zitat Allaire G, Jouve F, Michailidis G (2013) Casting constraints in structural optimization via a level-set method In: WCSMO-10, Orlando, Florida, USA Allaire G, Jouve F, Michailidis G (2013) Casting constraints in structural optimization via a level-set method In: WCSMO-10, Orlando, Florida, USA
Zurück zum Zitat Allaire G, Jouve F, Michailidis G (2016) Thickness control in structural optimization via a level set method. Struct Multidiscip Optim 53(6):1349–1382MathSciNetCrossRef Allaire G, Jouve F, Michailidis G (2016) Thickness control in structural optimization via a level set method. Struct Multidiscip Optim 53(6):1349–1382MathSciNetCrossRef
Zurück zum Zitat Bendsøe MP, Haber RB (1993) The Michell layout problem as a low volume fraction limit of the perforated plate topology optimization problem: an asymptotic study. Structural Optimization 6:263–267CrossRef Bendsøe MP, Haber RB (1993) The Michell layout problem as a low volume fraction limit of the perforated plate topology optimization problem: an asymptotic study. Structural Optimization 6:263–267CrossRef
Zurück zum Zitat Chen S, Wang MY, Liu AQ (2008) Shape feature control in structural topology optimization. Comput Aided Des 40:951–962CrossRef Chen S, Wang MY, Liu AQ (2008) Shape feature control in structural topology optimization. Comput Aided Des 40:951–962CrossRef
Zurück zum Zitat Choi KK, Chang KH (1994) A study of design velocity field computation for shape optimal design. Finite Elem Anal Des 15:317–341CrossRefMATH Choi KK, Chang KH (1994) A study of design velocity field computation for shape optimal design. Finite Elem Anal Des 15:317–341CrossRefMATH
Zurück zum Zitat Dunning PD (2018) Minimum length-scale constraints for parameterized implicit function based topology optimization. Struct Multidiscip Optim 58:155–169MathSciNetCrossRef Dunning PD (2018) Minimum length-scale constraints for parameterized implicit function based topology optimization. Struct Multidiscip Optim 58:155–169MathSciNetCrossRef
Zurück zum Zitat Dunning PD, Kim HA (2011) Investigation and improvement of sensitivity computation using the area-fraction weighted fixed grid FEM and structural optimization. Finite Elem Anal Des 47:933–941CrossRef Dunning PD, Kim HA (2011) Investigation and improvement of sensitivity computation using the area-fraction weighted fixed grid FEM and structural optimization. Finite Elem Anal Des 47:933–941CrossRef
Zurück zum Zitat Dunning PD, Kim HA (2015) Introducing the sequential linear programming level-set method for topology optimization. Struct Multidiscip Optim 51(3):631–643MathSciNetCrossRef Dunning PD, Kim HA (2015) Introducing the sequential linear programming level-set method for topology optimization. Struct Multidiscip Optim 51(3):631–643MathSciNetCrossRef
Zurück zum Zitat Garcia MJ, Steven GP (1998) Fixed grid finite elements in elasticity problems. Eng Comput 16(2):154–164 Garcia MJ, Steven GP (1998) Fixed grid finite elements in elasticity problems. Eng Comput 16(2):154–164
Zurück zum Zitat Guo X, Zhang W, Zhong W (2014) Explicit feature control in structural topology optimization via level set method. Comput Methods Appl Mech Eng 272:354–378MathSciNetCrossRefMATH Guo X, Zhang W, Zhong W (2014) Explicit feature control in structural topology optimization via level set method. Comput Methods Appl Mech Eng 272:354–378MathSciNetCrossRefMATH
Zurück zum Zitat Jang GW, Kim YY, Choi KK (2004) Remesh-free shape optimization using the wavelet-Galerkin method. Int J Solids Struct 41:6465–6483CrossRefMATH Jang GW, Kim YY, Choi KK (2004) Remesh-free shape optimization using the wavelet-Galerkin method. Int J Solids Struct 41:6465–6483CrossRefMATH
Zurück zum Zitat Kim HA, García MJ, Querin OM, Steven GP, Xie YM (2000) Introduction of fixed grid in evolutionary structural optimization. Eng Comput 17(4):427–439CrossRefMATH Kim HA, García MJ, Querin OM, Steven GP, Xie YM (2000) Introduction of fixed grid in evolutionary structural optimization. Eng Comput 17(4):427–439CrossRefMATH
Zurück zum Zitat Kim NH, Choi KK, Botkin ME (2003) Numerical method for shape optimization using meshfree method. Struct Multidiscip Optim 24:418–429CrossRef Kim NH, Choi KK, Botkin ME (2003) Numerical method for shape optimization using meshfree method. Struct Multidiscip Optim 24:418–429CrossRef
Zurück zum Zitat Liu J, Ma Y (2018) A new multi-material level set topology optimization method with the length scale control capability. Comput Methods Appl Mech Eng 329:444–463MathSciNetCrossRef Liu J, Ma Y (2018) A new multi-material level set topology optimization method with the length scale control capability. Comput Methods Appl Mech Eng 329:444–463MathSciNetCrossRef
Zurück zum Zitat Liu J, Ma Y, Fu J, Duke K (2015) A novel CACD/CAD/CAE integrated design framework for fiber-reinforced plastic parts. Adv Eng Softw 87:13–29CrossRef Liu J, Ma Y, Fu J, Duke K (2015) A novel CACD/CAD/CAE integrated design framework for fiber-reinforced plastic parts. Adv Eng Softw 87:13–29CrossRef
Zurück zum Zitat Liu P, Luo Y, Kang Z (2016) Multi-material topology optimization considering interface behavior via XFEM and level set method. Comput Methods Appl Mech Eng 308:113–133MathSciNetCrossRef Liu P, Luo Y, Kang Z (2016) Multi-material topology optimization considering interface behavior via XFEM and level set method. Comput Methods Appl Mech Eng 308:113–133MathSciNetCrossRef
Zurück zum Zitat Liu J, Li L, Ma Y (2018) Uniform thickness control without pre-specifying the length scale target under the level set topology optimization framework. Adv Eng Softw 115:204–216CrossRef Liu J, Li L, Ma Y (2018) Uniform thickness control without pre-specifying the length scale target under the level set topology optimization framework. Adv Eng Softw 115:204–216CrossRef
Zurück zum Zitat Luo J, Luo Z, Chen S, Tong L, Wang MY (2008) A new level set method for systematic design of hinge-free compliant mechanisms. Comput Methods Appl Mech Eng 198:318–331CrossRefMATH Luo J, Luo Z, Chen S, Tong L, Wang MY (2008) A new level set method for systematic design of hinge-free compliant mechanisms. Comput Methods Appl Mech Eng 198:318–331CrossRefMATH
Zurück zum Zitat Ozgun O, Kuzuoglu M (2016) Remesh-free shape optimization by transformation optics. IEEE Trans Antennas Propag 64:5479–5482CrossRef Ozgun O, Kuzuoglu M (2016) Remesh-free shape optimization by transformation optics. IEEE Trans Antennas Propag 64:5479–5482CrossRef
Zurück zum Zitat Rozvany GIN (1998) Exact analytical solutions for some popular benchmark problems in topology optimization. Structural Optimization 15:42–48CrossRefMATH Rozvany GIN (1998) Exact analytical solutions for some popular benchmark problems in topology optimization. Structural Optimization 15:42–48CrossRefMATH
Zurück zum Zitat Rozvany GIN, Ong TG, Szeto WT, Sandler R, Olhoff N, Bendsøe MP (1985) Least-weight design of perforated elastic plates. Int J Solids Struct 23:521–536CrossRefMATH Rozvany GIN, Ong TG, Szeto WT, Sandler R, Olhoff N, Bendsøe MP (1985) Least-weight design of perforated elastic plates. Int J Solids Struct 23:521–536CrossRefMATH
Zurück zum Zitat Sethian JA, Wingman A (2000) Structural boundary design via level set and immersed interface methods. J Comput Phys 163(2):489–528MathSciNetCrossRefMATH Sethian JA, Wingman A (2000) Structural boundary design via level set and immersed interface methods. J Comput Phys 163(2):489–528MathSciNetCrossRefMATH
Zurück zum Zitat Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim 21(2):120–127CrossRef Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim 21(2):120–127CrossRef
Zurück zum Zitat Wang Y, Kang Z (2018) A level set method for shape and topology optimization of coated structures. Comput Methods Appl Mech Eng 329:553–574MathSciNetCrossRef Wang Y, Kang Z (2018) A level set method for shape and topology optimization of coated structures. Comput Methods Appl Mech Eng 329:553–574MathSciNetCrossRef
Zurück zum Zitat Wang MY, Wang X (2004) “Color” level sets: a multi-phase method for structural topology optimization with multiple materials. Comput Methods Appl Mech Eng 193:469–496MathSciNetCrossRefMATH Wang MY, Wang X (2004) “Color” level sets: a multi-phase method for structural topology optimization with multiple materials. Comput Methods Appl Mech Eng 193:469–496MathSciNetCrossRefMATH
Zurück zum Zitat Wang MY, Wang XM, Guo DM (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192:227–246MathSciNetCrossRefMATH Wang MY, Wang XM, Guo DM (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192:227–246MathSciNetCrossRefMATH
Zurück zum Zitat Wang Y, Zhang L, Wang MY (2016) Length scale control for structural optimization by level sets. Comput Methods Appl Mech Eng 305:891–909MathSciNetCrossRefMATH Wang Y, Zhang L, Wang MY (2016) Length scale control for structural optimization by level sets. Comput Methods Appl Mech Eng 305:891–909MathSciNetCrossRefMATH
Zurück zum Zitat Xia Q, Shi T (2015) Constraints of distance from boundary to skeleton: for the control of length scale in level set based structural topology optimization. Comput Methods Appl Mech Eng 295:525–542MathSciNetCrossRefMATH Xia Q, Shi T (2015) Constraints of distance from boundary to skeleton: for the control of length scale in level set based structural topology optimization. Comput Methods Appl Mech Eng 295:525–542MathSciNetCrossRefMATH
Zurück zum Zitat Xia Q, Shi T (2016) Topology optimization of compliant mechanism and its support through a level set method. Comput Methods Appl Mech Eng 305:359–375MathSciNetCrossRefMATH Xia Q, Shi T (2016) Topology optimization of compliant mechanism and its support through a level set method. Comput Methods Appl Mech Eng 305:359–375MathSciNetCrossRefMATH
Zurück zum Zitat Xia Q, Wang MY, Shi T (2014) A level set method for shape and topology optimization of both structure and support of continuum structures. Comput Methods Appl Mech Eng 272:340–353MathSciNetCrossRefMATH Xia Q, Wang MY, Shi T (2014) A level set method for shape and topology optimization of both structure and support of continuum structures. Comput Methods Appl Mech Eng 272:340–353MathSciNetCrossRefMATH
Zurück zum Zitat Yamada T, Izui K, Nishiwaki S, Takezawa A (2010) A topology optimization method based on the level set method incorporating a fictitious interface energy. Comput Methods Appl Mech Eng 199:2876–2891MathSciNetCrossRefMATH Yamada T, Izui K, Nishiwaki S, Takezawa A (2010) A topology optimization method based on the level set method incorporating a fictitious interface energy. Comput Methods Appl Mech Eng 199:2876–2891MathSciNetCrossRefMATH
Zurück zum Zitat Yao TM, Choi KK (1989) 3-D shape optimal design and automatic finite element regridding. Int J Numer Methods Eng 28:369–384CrossRefMATH Yao TM, Choi KK (1989) 3-D shape optimal design and automatic finite element regridding. Int J Numer Methods Eng 28:369–384CrossRefMATH
Metadaten
Titel
Configuration optimization for thin structures using level set method
verfasst von
Gang-Won Jang
Sandilya Kambampati
Hayoung Chung
H. Alicia Kim
Publikationsdatum
28.03.2019
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 6/2019
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-019-02246-2

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