Engineering Transactions, 65, 1, pp. 61–67, 2017

Efficient Generator of Structural Topologies Based on Irregular Cellular Automata

Institute of Applied Mechanics, Cracow University of Technology

Institute of Applied Mechanics, Cracow University of Technology

Recent development of Cellular Automata implementation into optimal design problems has shown that the automaton can be an effective tool for generation of optimal topologies in engineering applications. Nevertheless, the vast majority of results have been obtained to date for regular lattices of cells. The aim of the present paper is therefore to extend the concept of Cellular Automata towards irregular grid of cells related to non-regular mesh of finite elements. Introducing irregular lattice of cells allows to reduce number of design variables without losing accuracy of results and without excessive increase of number of elements caused by using fine mesh for a whole structure. This paper proposes a novel Irregular Cellular Automata formulation that can be adapted to topology optimization of real structural elements. The effectiveness of proposed local update rule is illustrated by results of numerical generation of optimal topologies for selected spatial engineering structures.
Keywords: topology optimization; irregular cellular automata; local update rules
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


Bendsøe M.P., Kikuchi N., Generating optimal topologies in optimal design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, 71(2), 197–224, 1988, doi: 10.1016/0045-7825(88)90086-2.

Bendsøe M.P., Sigmund O., Topology optimization. Theory, methods and applications, Springer, Berlin – Heidelberg – New York 2004.

Bochenek B., Tajs-Zielińska K., Novel local rules of Cellular Automata applied to topology and size optimization, Engineering Optimization, 44(1): 23–35, 2012, doi: 10.1080/0305215X.2011.561843.

Bochenek B., Tajs-Zielińska K., Topology optimization with efficient rules of cellular automata, Engineering Computations, 30(8): 1086–1106, 2013, doi: 10.1108/EC-03-2012-0064.

Deaton J.D., Grandhi R.V., A survey of structural and multidisciplinary continuum topology optimization: post 2000, Structural and Multidisciplinary Optimization, 49(1): 1–38, 2014, doi: 10.1007/s00158-013-0956-z.

Inoue N., Shimotai N., Uesugi T., A cellular automaton generating topological structures, Proceedings SPIE, Proceedings of the 2nd European Conference on Smart Structures and Materials, 2361, 47–50, 1994, doi: 10.1117/12.184866.

Rozvany G.I.N., A critical review of established methods of structural topology optimization, Structural and Multidisciplinary Optimization, 37(3): 217–237, 2008, doi: 10.1007/s00158-007-0217-0.

Sigmund O., Maute K. Topology optimization approaches, Structural and Multidisciplinary Optimization, 48(6): 1031–1055, 2013, doi: 10.1007/s00158-013-0978-6.

Tovar A., Patel N.M., Niebur G.L., Sen M., Renaud J.E., Topology optimization using a hybrid cellular automaton method with local control rules, ASME Journal of Mechanical Design, 128(6): 1205–1216, 2006, doi: 10.1115/1.2336251.

DOI: 10.24423/engtrans.676.2017