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Interaction in Optimisation Problems: A Case Study in Truss Design

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Design Computing and Cognition '12

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Abstract

This paper is a preliminary study to explore the benefits of user interaction in topology optimisation by attempting to support two distinct claims: the first claim states that there exist similarly optimal, yet visually different designs based on the exact same parameters. The second one supports that accurately predicting the outcome can guide the program to faster convergence by skipping intermediary steps. For the purpose of this research a program based on Sigmund’s 99-line MATLAB code for topology optimisation was developed to implement real-time interaction. The programming language chosen was Java® for its flexibility and ease of scripting as well as its global efficiency. Both claims were tested through two distinct sets of experiments. The first one modified the designs by adding and/or removing material and proved the existence of similarly optimal yet different designs. The second one explored the use of pseudo-filters to simulate intuition and managed significant decreases in the amount of iterations necessary for convergence. This second experiment also produced slightly stiffer designs. Both experiments led to the conclusion that user interaction, when used responsibly, helps topology optimisation in generating creativity and in speeding the process.

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Notes

  1. 1.

    In order to be able to make a choice based on aesthetical reasons.

  2. 2.

    See the parts on future improvements and limitations for more information on resource constraints.

  3. 3.

    Triangles represent hinges; bars represent boundary conditions for a whole side and the thin arrows under those bars show the direction in which displacements are blocked; thick arrows represent a downwards unitary force.

  4. 4.

    It might useful to note that the intervention of a user mid-way through the optimisation process is a special case of changing the initial start point for optimisation.

  5. 5.

    These pseudo-filters have a role similar to actual filters but work with threshold values rather than neighbouring cells.

  6. 6.

    Defined as “areas where the density jumps from 0 to 1 between neighbouring elements” (Pedersen et al. 2006: 1), the checkerboard patterns are a common numerical instability that occurs particularly when using Q4 elements [12].

  7. 7.

    This case is the 4-corners case for which the solution provided by the program is far from the optimal one. It is only a marginal result and should thus be disregarded.

  8. 8.

    This result corresponds to the one mentioned in the previous footnote.

  9. 9.

    The reason the original design is unsymmetrical is the slight upward shift in the concentrated load. Indeed, it is not applied on the middle node but on the one above it.

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Author information

Authors and Affiliations

  1. University College London, London, UK

    Simon de Timary & Sean Hanna

Authors
  1. Simon de Timary
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  2. Sean Hanna
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Corresponding author

Correspondence to Simon de Timary .

Editor information

Editors and Affiliations

  1. Krasnow Institute for Advanced Study, Fairfax, Virginia, USA

    John S. Gero

Appendix: Design Families

Appendix: Design Families

See Figs. 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29 and 30.

Fig. 19
figure 19

4-corners, family 1, deviation 6.2 %, compliance +0.13 %

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Fig. 20
figure 20

4-corners, fam. 2, dev. 47.3 %, comp. −25.8 %

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Fig. 21
figure 21

Cantilever, fam. 1, dev. 7.1 %, comp. −0.12 %

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Fig. 22
figure 22

Cantilever, fam. 2, dev. 15 %, comp. −0.25 %

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Fig. 23
figure 23

Cantilever, fam. 3, dev. 14 %, comp. −0.11 %

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Fig. 24
figure 24

Cantilever, fam. 6, dev. 25.2 %, comp. +2.9 %

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Fig. 25
figure 25

MBB, fam. 1, dev. 22 %, comp. +0.05 %

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Fig. 26
figure 26

MBB, fam. 2, dev. 14.3 %, comp. +1.0 %

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Fig. 27
figure 27

MBB, fam. 5, dev. 26.2 %, comp. −1.73 %

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Fig. 28
figure 28

Michell-1, fam. 5, dev. 39.1 %, comp. +53.8 %

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Fig. 29
figure 29

Michell-2, fam. 4, dev. 13.6 %, comp. −1.3 %

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Fig. 30
figure 30

Michell-2, fam. 5, dev. 15.5 %, comp. +2.1 %

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de Timary, S., Hanna, S. (2014). Interaction in Optimisation Problems: A Case Study in Truss Design. In: Gero, J. (eds) Design Computing and Cognition '12. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9112-0_11

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  • DOI: https://doi.org/10.1007/978-94-017-9112-0_11

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-9111-3

  • Online ISBN: 978-94-017-9112-0

  • eBook Packages: EngineeringEngineering (R0)

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