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Cellular Automata for Simultaneous Analysis and Optimal Structural Topology Design

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Simulating Complex Systems by Cellular Automata

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

The Cellular Automata (CA) paradigm has been finding more and more applications in engineering and sciences in the past decade, but nevertheless its use for engineering design has not been widely popular. The proposed chapter is a special and unique implementation of the paradigm for combined analysis and design of continuum structures made of isotropic and fiber reinforced orthotropic materials. In particular, the use of a computational approach for topology design of the structural domain together with its local field and design variables is discussed.

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References

  1. E. Kita, T. Toyoda, Structural design using cellular automata. Struct. Multidiscip. Optim. 19, 64–73 (2000)

    Article  Google Scholar 

  2. Y.M. Xie, G.P. Steven, A simple evolutionary procedure for structural optimization. Comput. Struct. 49, 885–896 (1993)

    Article  Google Scholar 

  3. C. Zhao, G.P. Steven, Y.M. Xie, Effect of initial non-design domain on optimal topologies of structures during natural frequency optimization. Comput. Struct. 62, 119–131 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  4. Z. Gürdal, B. Tatting, Cellular automata for design of truss structures with linear and non linear response. In 41st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Atlanta, GA, 2000

    Google Scholar 

  5. R.T. Haftka, Z. Gürdal, Elements of Structural Optimization. (Kluwer, Dordrecht, 1993)

    Google Scholar 

  6. B. Tatting, Z. Gürdal, Cellular automata for design of two-dimensional continuum structures. In 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Long Beach, CA, 2003

    Google Scholar 

  7. M.M. Abdalla, Z. Gürdal, Structural design using cellular automata for eigenvalue problems. Struct. Multidiscip. Optim. 26, 200–208 (2004)

    Article  Google Scholar 

  8. M.M. Abdalla, Z. Gürdal, Structural design using optimality based cellular automata. In 43th AIAA/ASME/ AHS/ASC Structures, Structural Dynamics and material Conference, Denver, Co, April 2002

    Google Scholar 

  9. M. P. Bendsøe. Optimal shape design as a material distribution problem. Struct. Multidiscip. Optimi. 1, 193–200 (1989)

    Article  Google Scholar 

  10. M. Zhou, G.I.N. Rozvany, The coc algorithm, part ii: Topological, geometry and generalized shape optimization. Comput. Meth. Appl. Mechan. Eng. 89, 197–224 (1991)

    Article  Google Scholar 

  11. G.I.N. Rozvany, M. Zhou, T. Birker, Generalized shape optimization without homogenization. Struct. Multidiscip. Optim. 4, 250–252 (1992)

    Article  Google Scholar 

  12. G.I.N. Rozvany, Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics. Struct. Multidiscip. Optim. 21, 90–108 (2001)

    Article  Google Scholar 

  13. O. Sigmund, A 99 line topology optimization code written in matlab. Struct. Multidiscip. Optim. 21, 120–127 (2001)

    Article  Google Scholar 

  14. S. Setoodeh, M.M. Abdalla, Z. Gürdal, Combined topology and fiber path design of composite layers using cellular automata. Struct. Multidiscip. Optim. 30, 413–421 (2005)

    Article  Google Scholar 

  15. R. Zakhama, M.M. Abdalla, H. Smaoui, Z. Gürdal, Topology design of geometrically nonlinear 2d elastic continua using ca and an equivalent truss model. In 11th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Portsmouth, VA 2006

    Google Scholar 

  16. D.J. Slotta, B. Tatting, L.T. Watson, Z. Gürdal, S. Missoum, Convergence analysis for cellular automata applied to truss design. Eng. Comput. 19, 953–969 (2002)

    Article  MATH  Google Scholar 

  17. S. Setoodeh, D.B. Adams, Z. Gürdal, L.T. Watson, Pipeline implementation of cellular automata for structural design on message-passing multiprocessors. Math. Comput. Model. 43, 966–975 (2006)

    Article  MATH  Google Scholar 

  18. S. Kim, M.M. Abdalla, Z. Gürdal, M. Jones, Multigrid accelerated cellular automata for structural design optimization: A 1-d implementation. In 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Palm Springs, CA, 2004

    Google Scholar 

  19. R. Zakhama, M.M. Abdalla, H. Smaoui, Z. Gürdal, Multigrid implementation of cellular automata for topology optimization of continuum structures. CMES: Computer Modeling in Engineering and Sciences, to appear, 2010

    Google Scholar 

  20. P. Wesseling, An introduction to multigrid methods. (Wiley, Chichester, 1992)

    Google Scholar 

  21. A. Tovar, N.M. Patel, G.L. Niebur, M. Sen, J.E. Renaud. Topology optimization using a hybrid cellular automaton method with local control rules. J. Mechan. Des. 128(6), 1205–1216 (2006)

    Article  Google Scholar 

  22. A. Tovar, N.M. Patel, A.K. Kaushik, J.E. Renaud, Optimality conditions of the hybrid cellular automata for structural optimization. AIAA J. 45(3), 673–683 (2007)

    Article  Google Scholar 

  23. S. Missoum, M.M. Abdalla, Z. Gürdal, Nonlinear topology design of trusses using cellular automata. In 44th AIAA/ASME/AHS/ASC Symposium on Structural Dynamics and Material Conference, Norfolk, VA, 2003

    Google Scholar 

  24. S. Missoum, M.M. Abdalla, Z. Gürdal, Nonlinear design of trusses under multiple loads using cellular automata. In 5th World Congress in Structural and Multidisciplinary Optimization, Lido diJesolo, Italy, 2003

    Google Scholar 

  25. S. Setoodeh, Z. Gürdal, L.T. Watson. Design of variable-stiffness composite layers using cellular automata. Comput. Meth. Appl. Mechan. Eng. 195, 836–851 (2006)

    Article  MATH  Google Scholar 

  26. N.V. Banichuk, Optimization of anisotropic properties of deformable media in plane problems of elasticity. Mesh Solids, 14, 63–68 (1979)

    Google Scholar 

  27. P. Pedersen. Bounds on elastic energy in solids of orthotropic materials. Struct. Optim. 2, 55–63 (1990)

    Article  Google Scholar 

  28. M. Beckers, Topology optimization using a dual method with discrete variables. Struct. Optim. 17, 14–24 (1999)

    Article  MathSciNet  Google Scholar 

  29. M.P. Bendsøe, O. Sigmund, Topology Optimization, Theory, Methods and Applications (Springer-Verlag, 2003)

    Google Scholar 

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Correspondence to Zafer Gürdal .

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Gürdal, Z., Zakhama, R. (2010). Cellular Automata for Simultaneous Analysis and Optimal Structural Topology Design. In: Kroc, J., Sloot, P., Hoekstra, A. (eds) Simulating Complex Systems by Cellular Automata. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12203-3_14

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  • DOI: https://doi.org/10.1007/978-3-642-12203-3_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12202-6

  • Online ISBN: 978-3-642-12203-3

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