Abstract
To determine the stability of LEGO® structures is an interesting problem because the special binding mechanism prohibits the usage of methods of structural frame design or dynamic physics engines. We propose a new two-phase approach where instances of maximum-flow networks are constructed. In a first phase, the distribution of compressive and tensile forces is computed which is used in a second phase to model the moments within the structure. By solving the maximum-flow networks we can use the resulting flow as a sufficient criterion for the stability of the structure. The approach is demonstrated for two exemplary structures which outperform previous results using a multi-commodity flow network.
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References
Cherkassky, B.V., Goldberg, A.V.: On implementing the push-relabel method for the maximum flow problem. Algorithmica 19, 390–410 (1997)
Edmonds, J., Karp, R.M.: Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the ACM 19(2), 248–264 (1972)
Funes, P., Pollack, J.B.: Computer evolution of buildable objects. In: Husbands, P., Harvey, I. (eds.) Fourth European Conf. on Artificial Life, pp. 358–367. MIT Press, Cambridge (1997)
Funes, P., Pollack, J.B.: Computer evolution of buildable objects. In: Bentley, P.J. (ed.) Evolutionary Design by Computers, pp. 387–403. Morgan Kaufmann, San Francisco (1999)
Funes, P.J.: Buildable evolution. SIGEVOlution 2(3), 6–19 (2007)
Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum flow problem. Journal of the ACM 35, 921–940 (1988)
Waßmann, M.: Physiksimulation und Evolution von LEGO®-Strukturen. Master’s thesis, HTWK Leipzig, Leipzig, Germany (2011)
Waßmann, M., Weicker, K.: Buildable objects revisited. To appear in PPSN 2012 – 12th International Conference on Parallel Problem Solving from Nature. Springer, Heidelberg (2012)
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Waßmann, M., Weicker, K. (2012). Maximum Flow Networks for Stability Analysis of LEGO®Structures. In: Epstein, L., Ferragina, P. (eds) Algorithms – ESA 2012. ESA 2012. Lecture Notes in Computer Science, vol 7501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33090-2_70
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DOI: https://doi.org/10.1007/978-3-642-33090-2_70
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33089-6
Online ISBN: 978-3-642-33090-2
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