Advertisement

Interactive topology optimization on hand-held devices

  • Niels AageEmail author
  • Morten Nobel-Jørgensen
  • Casper Schousboe Andreasen
  • Ole Sigmund
Educational Article

Abstract

This paper presents an interactive topology optimization application designed for hand-held devices running iOS or Android. The TopOpt app solves the 2D minimum compliance problem with interactive control of load and support positions as well as volume fraction. Thus, it is possible to change the problem settings on the fly and watch the design evolve to a new optimum in real time. The use of an interactive app makes it extremely simple to learn and understand the influence of load-directions, support conditions and volume fraction. The topology optimization kernel is written in C# and the graphical user interface is developed using the game engine Unity3D. The underlying code is inspired by the publicly available 88 and 99 line Matlab codes for topology optimization but does not utilize any low-level linear algebra routines such as BLAS or LAPACK. The TopOpt App can be downloaded on iOS devices from the Apple App Store, at Google Play for the Android platform, and a web-version can be run from www.topopt.dtu.dk.

Keywords

Interactiveness Topology optimization Smartphones Tablets PDE constrained optimization 

Notes

Acknowledgments

The authors would like to extend their gratitude to the members of the TopOpt and NextTop groups at DTU for their invaluable input on the design and testing of the TopOpt app.

References

  1. Amir O, Sigmund O (2011) On reducing computational effort in topology optimization: how far can we go? Struct Multidisc Optim 44:25–29CrossRefGoogle Scholar
  2. Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O (2010) Efficient topology optimization in MATLAB using 88 lines of code. Struct Multidisc Optim 43(1):1–16CrossRefGoogle Scholar
  3. Arioli M (2004) A stopping criterion for the conjugate gradient algorithm in a finite element method framework. Numer Math 97:1–24MathSciNetzbMATHCrossRefGoogle Scholar
  4. Bendsøe M (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202CrossRefGoogle Scholar
  5. Bendsøe M, Sigmund O (2004) Topology optimization; theory, methods and applications, 2nd edn. Springer, Berlin Heidelberg New YorkzbMATHGoogle Scholar
  6. Bourdin B (2001) Filters in topology optimization. Int J Numer Methods Eng 50(9):2143–2158MathSciNetzbMATHCrossRefGoogle Scholar
  7. Bruns TE, Tortorelli DA (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190(26–27):3443–3459zbMATHCrossRefGoogle Scholar
  8. Mlejnek HP (1992) Some aspects of the genesis of structures. Struct Optim 5:64–69CrossRefGoogle Scholar
  9. Nguyen TH, Paulino GH, Song J, Le CH (2010) A computational paradigm for multiresolution topology optimization (mtop). Struct Multidisc Optim 41:525–539MathSciNetCrossRefGoogle Scholar
  10. Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mechan Struct Mach 25(4):493–525CrossRefGoogle Scholar
  11. Sigmund O (2001) A 99 line topology optimization code written in MATLAB. Struct Multidisc Optim 21(2):120–127CrossRefGoogle Scholar
  12. Statistics Denmark (2012) http://www.dst.dk/statistik/nyt/emneopdelt.aspx?psi=1409. Accessed 14 Jun 2012
  13. Stolpe M, Svanberg K (2001) An alternative interpolation scheme for minimum compliance topology optimization. Struct Multidisc Optim 22(2):116–124CrossRefGoogle Scholar
  14. Tcherniak D, Sigmund O (2001) A web-based topology optimization program. Struct Multidisc Optim 22(3):179–187CrossRefGoogle Scholar
  15. Unity Technologies (2012) Unity3d. www.unity3d.com. Accessed 20 Mar 2012
  16. Wang F, Lazarov B, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidisc Optim 43(6):767–784CrossRefGoogle Scholar
  17. Zhou M, Rozvany GIN (1991) The COC algorithm, part II: topological, geometry and generalized shape optimization. Comput Methods Appl Mech Eng 89(1–3):309–336CrossRefGoogle Scholar
  18. Zienkiewicz OC, Taylor RL (2000) Finite element method, vol 1, 5th edn. Butterworth-HeinemannGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Niels Aage
    • 1
    Email author
  • Morten Nobel-Jørgensen
    • 2
  • Casper Schousboe Andreasen
    • 1
  • Ole Sigmund
    • 1
  1. 1.Department of Mechanical Engineering, Solid MechanicsTechnical University of DenmarkKgs. LyngbyDenmark
  2. 2.Department of Informatics and Mathematical ModellingTechnical University of DenmarkKgs. LyngbyDenmark

Personalised recommendations