Skip to main content

2019 | OriginalPaper | Buchkapitel

Combined Length Scale and Overhang Angle Control in Minimum Compliance Topology Optimization for Additive Manufacturing

verfasst von : Jeroen Pellens, Geert Lombaert, Boyan Lazarov, Mattias Schevenels

Erschienen in: EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This paper focusses on topology optimization for additive manufacturing. Two manufacturing constraints are considered: minimum length scale and maximum overhang angle. The first is needed to ensure that the condition on minimal printable feature sizes is satisfied, while the second eliminates the need for a temporary support structure. Filtering schemes have been proposed in the literature to ensure either a minimum length scale or a maximum overhang angle, but not both simultaneously. In this paper, it is shown that both constraints cannot simultaneously be met by simply applying both filters sequentially, as the effect of the first filter is destroyed by the second. A new, slightly more complex filtering scheme is therefore proposed, which does allow simultaneous control over length scale and overhang angle in a minimum compliance topology optimization problem. The method is successfully applied to a 2D benchmark problem.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Rosen, D.: Design for additive manufacturing: past, present, and future directions. J. Mech. Des. 136 (2014) Rosen, D.: Design for additive manufacturing: past, present, and future directions. J. Mech. Des. 136 (2014)
2.
Zurück zum Zitat Bendsøe, M.P.: Optimal shape design as a material distribution problem. Struct. Multi. Optim. 1(4), 193–202 (1989)MathSciNetCrossRef Bendsøe, M.P.: Optimal shape design as a material distribution problem. Struct. Multi. Optim. 1(4), 193–202 (1989)MathSciNetCrossRef
3.
Zurück zum Zitat Zhou, M., Rozvany, G.I.N.: The COC algorithm, part II: topological, geometrical and generalized shape optimization. Comput. Methods Appl. Mech. Eng. 89(1–3), 309–336 (1991)CrossRef Zhou, M., Rozvany, G.I.N.: The COC algorithm, part II: topological, geometrical and generalized shape optimization. Comput. Methods Appl. Mech. Eng. 89(1–3), 309–336 (1991)CrossRef
4.
Zurück zum Zitat Díaz, A.R., Sigmund, O.: Checkerboard patterns in layout optimization. Struct. Optim. 10(1), 40–45 (1995)CrossRef Díaz, A.R., Sigmund, O.: Checkerboard patterns in layout optimization. Struct. Optim. 10(1), 40–45 (1995)CrossRef
5.
Zurück zum Zitat Jog, C.S., Haber, R.B.: Stability of finite element models for distributed-parameter optimization and topology design. Comput. Methods Appl. Mech. Eng. 130(3–4), 203–226 (1996)MathSciNetCrossRef Jog, C.S., Haber, R.B.: Stability of finite element models for distributed-parameter optimization and topology design. Comput. Methods Appl. Mech. Eng. 130(3–4), 203–226 (1996)MathSciNetCrossRef
6.
Zurück zum Zitat Bruns, T.E., Tortorelli, D.A.: Topology optimization of non-linear elastic structures and compliant mechanisms. Comput. Methods Appl. Mech. Eng. 190(26–27), 3443–3459 (2001)CrossRef Bruns, T.E., Tortorelli, D.A.: Topology optimization of non-linear elastic structures and compliant mechanisms. Comput. Methods Appl. Mech. Eng. 190(26–27), 3443–3459 (2001)CrossRef
7.
8.
Zurück zum Zitat Guest, J.K., Prevost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int. J. Numer. Methods Eng. 61(2), 238–254 (2004)MathSciNetCrossRef Guest, J.K., Prevost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int. J. Numer. Methods Eng. 61(2), 238–254 (2004)MathSciNetCrossRef
9.
Zurück zum Zitat Xu, S.L., Cai, Y.W., Cheng, G.D.: Volume preserving nonlinear density filter based on Heaviside functions. Struct. Multi. Optim. 41(4), 495–505 (2010)MathSciNetCrossRef Xu, S.L., Cai, Y.W., Cheng, G.D.: Volume preserving nonlinear density filter based on Heaviside functions. Struct. Multi. Optim. 41(4), 495–505 (2010)MathSciNetCrossRef
10.
Zurück zum Zitat Sigmund, O.: Morphology-based black and white filters for topology optimization. Struct. Multi. Optim. 33(4–5), 401–424 (2007)CrossRef Sigmund, O.: Morphology-based black and white filters for topology optimization. Struct. Multi. Optim. 33(4–5), 401–424 (2007)CrossRef
11.
Zurück zum Zitat Pratt, W.K.: Digital Image Processing. Wiley (1991) Pratt, W.K.: Digital Image Processing. Wiley (1991)
12.
Zurück zum Zitat Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Struct. Multi. Optim. 43(6), 767–784 (2011)CrossRef Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Struct. Multi. Optim. 43(6), 767–784 (2011)CrossRef
13.
Zurück zum Zitat Lazarov, B.S., Wang, F., Sigmund, O.: Length scale and manufacturability in density-based topology optimization. Arch. Appl. Mech. 86(1–2), 189–218 (2016)CrossRef Lazarov, B.S., Wang, F., Sigmund, O.: Length scale and manufacturability in density-based topology optimization. Arch. Appl. Mech. 86(1–2), 189–218 (2016)CrossRef
14.
Zurück zum Zitat Wadbro, E., Hägg, L.: On length scale control in topology optimization. WCSMO (2017) Wadbro, E., Hägg, L.: On length scale control in topology optimization. WCSMO (2017)
15.
Zurück zum Zitat Gibson, I., Rosen, D., Stucker, B.: Additive Manufacturing Technologies. Springer (2015) Gibson, I., Rosen, D., Stucker, B.: Additive Manufacturing Technologies. Springer (2015)
16.
Zurück zum Zitat Atzeni, E., Salmi, A.: Economics of additive manufacturing for end-usable metal parts. Int. J. Adv. Manuf. Technol. 62, 1147–1155 (2012)CrossRef Atzeni, E., Salmi, A.: Economics of additive manufacturing for end-usable metal parts. Int. J. Adv. Manuf. Technol. 62, 1147–1155 (2012)CrossRef
17.
Zurück zum Zitat Becker, R., Grzesiak, A., Henning, A.: Rethink assembly design. Assembly Autom. 25(4), 262–266 (2005)CrossRef Becker, R., Grzesiak, A., Henning, A.: Rethink assembly design. Assembly Autom. 25(4), 262–266 (2005)CrossRef
18.
Zurück zum Zitat Cormier, D., Harrysson, T., Mahale, O.: Rapid manufacturing in the 21st century. J. Chin. Inst. Ind. Eng. 20(3), 193–202 (2003) Cormier, D., Harrysson, T., Mahale, O.: Rapid manufacturing in the 21st century. J. Chin. Inst. Ind. Eng. 20(3), 193–202 (2003)
19.
Zurück zum Zitat Liu, J., Ma, Y.: A survey of manufacturing oriented topology optimization methods. Adv. Eng. Softw., 161–175 (2016) Liu, J., Ma, Y.: A survey of manufacturing oriented topology optimization methods. Adv. Eng. Softw., 161–175 (2016)
20.
Zurück zum Zitat Brackett, D., Ashcroft, I., Hague, R.: Topology optimization for additive manufacturing. In: Proceedings of the Solid Freeform Fabrication Symposium, Austin, TX, US, pp. 348–362 (2011) Brackett, D., Ashcroft, I., Hague, R.: Topology optimization for additive manufacturing. In: Proceedings of the Solid Freeform Fabrication Symposium, Austin, TX, US, pp. 348–362 (2011)
21.
Zurück zum Zitat Gaynor, A.T., Guest, J.K.: Topology optimization for additive manufacturing: considering maximum overhang constraint. In: 15th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, pp. 16–20 (2014) Gaynor, A.T., Guest, J.K.: Topology optimization for additive manufacturing: considering maximum overhang constraint. In: 15th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, pp. 16–20 (2014)
22.
Zurück zum Zitat Qian, X.: Undercut and overhang angle control in topology optimization: a density gradient based integral approach. Int. J. Numer. Methods Eng. (2017) Qian, X.: Undercut and overhang angle control in topology optimization: a density gradient based integral approach. Int. J. Numer. Methods Eng. (2017)
23.
Zurück zum Zitat Langelaar, M.: An additive manufacturing filter for topology optimization of print-ready designs. Struct. Multi. Optim., July 2016 Langelaar, M.: An additive manufacturing filter for topology optimization of print-ready designs. Struct. Multi. Optim., July 2016
24.
Zurück zum Zitat Wang, D., Yang, Y., Yi, Z., Su, X.: Research on the fabricating quality optimization of the overhanging surface in slm process. Int. J. Adv. Manuf. Technol. 65, 1471–1484 (2013)CrossRef Wang, D., Yang, Y., Yi, Z., Su, X.: Research on the fabricating quality optimization of the overhanging surface in slm process. Int. J. Adv. Manuf. Technol. 65, 1471–1484 (2013)CrossRef
25.
Zurück zum Zitat Kranz, J., Herzog, D., Emmelmann, C.: Design guidelines for laser additive manufacturing of lightweight structures in tial6v4. J. Laser Appl. 27 (2015) Kranz, J., Herzog, D., Emmelmann, C.: Design guidelines for laser additive manufacturing of lightweight structures in tial6v4. J. Laser Appl. 27 (2015)
26.
Zurück zum Zitat Langelaar, M.: Topology optimization of 3D self-supporting structures for additive manufacturing. Add. Manuf. 12(A), 60–70 (2016) Langelaar, M.: Topology optimization of 3D self-supporting structures for additive manufacturing. Add. Manuf. 12(A), 60–70 (2016)
Metadaten
Titel
Combined Length Scale and Overhang Angle Control in Minimum Compliance Topology Optimization for Additive Manufacturing
verfasst von
Jeroen Pellens
Geert Lombaert
Boyan Lazarov
Mattias Schevenels
Copyright-Jahr
2019
DOI
https://doi.org/10.1007/978-3-319-97773-7_33

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.