Structural and Multidisciplinary Optimization

, Volume 56, Issue 2, pp 473–485 | Cite as

Topology optimization for finding shell structures manufactured by deep drawing



This paper presents a new approach for optimizing shell structures considering their mid surface design including cut-outs. Therefore we introduced a manufacturing constraint to the 3D topology optimization based on the density method in order to receive an optimized structure without undercuts and with a constant wall thickness, so that these structures can be manufactured by deep drawing in one step. It is shown that introducing cut-outs while increasing the shell thickness can improve the performance of shell structures considering their stiffness at a constant mass.


Topology optimization Sheet metals Deep drawing Manufacturing constraint Thin walled structures 


  1. Allaire G, Jouve F, Michailidis G (2013) Casting constraints in structural optimization via level-set method. Proc. of 10th World Congress on Structural and Multidisciplinary Optimization, Orlando, USAGoogle Scholar
  2. Ansola R, Canales J, Tarrago JA, Rasmussen J (2002) On simultaneous shape and material layout optimization of shell structures. Struct Multidiscip Optim 24:175–184CrossRefGoogle Scholar
  3. Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202CrossRefGoogle Scholar
  4. Bertsch C, Cislino AP, Langer S, Reese S (2008) Topology optimization of 3D elastic structures using boundary elements. Proc Appl Math Mech 8:10771–10772CrossRefGoogle Scholar
  5. Bletzinger KU, Ramm E (2014) A consistent frame for sensitivity filtering and the vertex assigned morphing of optimal shape. Struct Multidiscip Optim 49:873–895MathSciNetCrossRefGoogle Scholar
  6. Boljanovic V (2014) Sheet metal forming processes and die design. Industrial Press, South NorwalkGoogle Scholar
  7. Dienemann R, Schumacher A, Fiebig S (2016) Topology and shape optimization of sheet metals with integrated deep-drawing-simulation. Proc. of 12th World Conference on Computational Mechanics, Seoul, KoreaGoogle Scholar
  8. Falkenberg P, Franke T, Fiebig S, Vietor T (2015) Consideration of adhesive joints for a multi-material topology optimization approach, 20th International Conference on Composite Materials, Copenhagen, DenmarkGoogle Scholar
  9. Fiebig S, Sellschopp J, Manz H, Vietor T, Axmann K, Schumacher A (2015) Future challenges for topology optimization for the usage in automotive lightweight design technologies. Proc. of 11th World Congress on Structural and Multidisciplinary Optimization, Sydney, AustraliaGoogle Scholar
  10. Fleury C (1989) CONLIN: an efficient dual optimizer based on convex approximation concepts. Struct Optim 1:81–89CrossRefGoogle Scholar
  11. Franke T, Vietor T, Fiebig S, Horstmann GM (2015) Robust and production-oriented topology optimization of cast parts including manufacturing restrictions and process simulation, NAFEMS seminar Optimierung und Robust Design, Wiesbaden, GermanyGoogle Scholar
  12. Guest J, Zhu M (2012) Casting and milling restrictions in topology optimization via projection-based algorithms. Proceedings of the ASME 2012 International Design Engineering Technical Conference & Computers and Information in Engineering Conference, Chicago, IL, USAGoogle Scholar
  13. Harzheim L, Graf G (2006) A review of optimization of cast parts using topology optimization II—topology optimization with manufacturing constraints. Struct Multidiscip Optim 31:388–399CrossRefGoogle Scholar
  14. Hassani B, Tavakkoli SM, Ghasemnejad H (2013) Simultaneous shape and topology optimization of shell structures. Struct Multidiscip Optim 48:221–233MathSciNetCrossRefMATHGoogle Scholar
  15. Le C, Norato J, Bruns T, Ha C, Tortorelli D (2010) Stress-based topology optimization for continua. Struct Multidiscip Optim 41:605–620CrossRefGoogle Scholar
  16. Lochner-Aldinger I, Schumacher A (2014) Homogenization method. In: Adriaenssens S, Block P, Veenendaal D, Williams C (eds) Shell structures for architecture—form finding and optimization. Routledge, New YorkGoogle Scholar
  17. Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Multidiscip Optim 16:68–75CrossRefGoogle Scholar
  18. Sigmund O, Aage N, Andreassen, E (2016) On the (non-) optimality of Michell structures. Struct Multidiscip Optim 54(2):361–373Google Scholar
  19. Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24:359–373MathSciNetCrossRefMATHGoogle Scholar
  20. Xia Q, Shi T, Wang MY, Liu S (2009) A level set based method for the optimization of cast part. Struct Multidiscip Optim 41:735–747CrossRefGoogle Scholar
  21. Zhou M, Fleury F, Patten S, Stannard N, Mylett D, Gardner S (2011) Topology optimization—practical aspects for industrial applications. Proc. of 9th World Congress on Structural and Multidisciplinary Optimization, Shizuoka, JapanGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.University of WuppertalWuppertalGermany
  2. 2.Volkswagen AG, BraunschweigLower SaxonyGermany

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