Topology optimization with efficient rules of cellular automata

Purpose – Biologically inspired techniques like cellular automata (CA) are gaining nowadays attention of designers. This is because they are effective, do not require gradient information, and one can easily combine this type of algorithm with any finite element structural analysis code. The purpose of this paper is to develop a CA algorithm based on novel local rules oriented at solving compliance-based topology optimization problems. Design/methodology/approach – The design domain is divided into lattice of cells, states of which are updated synchronously. The proposed rules include information coming from an individual cell and from its neighborhood, and by introducing weighting parameters allow to control and modify topology generation process. Findings – The performance of the developed algorithm is very satisfactory, and a comparison with results of other authors, obtained with the use of various optimization techniques, shows efficiency of the present topology generation process. The results found ...

[1]  G. Allaire,et al.  Structural optimization using sensitivity analysis and a level-set method , 2004 .

[2]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[3]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[4]  Yi Min Xie,et al.  A further review of ESO type methods for topology optimization , 2010 .

[5]  Tomasz Arciszewski,et al.  Emergent engineering design: design creativity and optimality inspired by nature , 2004 .

[6]  O. Sigmund,et al.  Filters in topology optimization based on Helmholtz‐type differential equations , 2011 .

[7]  Naoko Shimotai,et al.  Cellular automaton generating topological structures , 1994, Other Conferences.

[8]  Katarzyna Tajs-Zielińska,et al.  Novel local rules of cellular automata applied to topology and size optimization , 2012 .

[9]  Niels Olhoff,et al.  Topology optimization of continuum structures: A review* , 2001 .

[10]  M. Bendsøe Optimal shape design as a material distribution problem , 1989 .

[11]  Kepeng Qiu,et al.  Bi-Directional Evolutionary Topology Optimization Using Element Replaceable Method , 2007 .

[12]  M. Zhou,et al.  The COC algorithm, Part II: Topological, geometrical and generalized shape optimization , 1991 .

[13]  Osvaldo M. Querin,et al.  Topology design of three-dimensional continuum structures using isosurfaces , 2011, Adv. Eng. Softw..

[14]  A. Lindenmayer Mathematical models for cellular interactions in development. I. Filaments with one-sided inputs. , 1968, Journal of theoretical biology.

[15]  Grant P. Steven,et al.  Effective optimisation of continuum topologies through a multi-GA system , 2005 .

[16]  W. R. Stahl Self-Reproducing Automata , 2015, Perspectives in biology and medicine.

[17]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

[18]  Aristid Lindenmayer,et al.  Mathematical Models for Cellular Interactions in Development , 1968 .

[19]  Ole Sigmund,et al.  A 99 line topology optimization code written in Matlab , 2001 .

[20]  Leonard Spunt,et al.  Optimum structural design , 1971 .

[21]  John E. Renaud,et al.  Topology Optimization Using a Hybrid Cellular Automaton Method With Local Control Rules , 2006 .

[22]  Anders Clausen,et al.  Efficient topology optimization in MATLAB using 88 lines of code , 2011 .

[23]  Norio Inou,et al.  Super-mechano-colony self-organizing a mechanical structure , 1999, IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028).

[24]  A ROSENBLUETH,et al.  The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle. , 1946, Archivos del Instituto de Cardiologia de Mexico.

[25]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .

[26]  Raúl A. Feijóo,et al.  Topological Sensitivity Analysis for Three-dimensional Linear Elasticity Problem , 2007 .