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Structural topology optimization using a genetic algorithm with a morphological geometric representation scheme

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Abstract

This paper describes a versatile methodology for solving topology design optimization problems using a genetic algorithm (GA). The key to its effectiveness is a geometric representation scheme that works by specifying a skeleton which defines the underlying topology/connectivity of a structural continuum together with segments of material surrounding the skeleton. The required design variables are encoded in a chromosome which is in the form of a directed graph that embodies this underlying topology so that appropriate crossover and mutation operators can be devised to recombine and help preserve any desirable geometry characteristics of the design through succeeding generations in the evolutionary process. The overall methodology is first tested by solving ‘target matching’ problems—simulated topology optimization problems in each of which a ‘target’ geometry is first created and predefined as the optimum solution, and the objective of the optimization problem is to evolve design solutions to converge towards this target shape. The methodology is then applied to design two path-generating compliant mechanisms—large-displacement flexural structures that undergo some desired displacement paths at some point when given a straight line input displacement at some other point—by an actual process of topology/shape optimization.

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References

  1. Akhtar S, Tai K, Prasad J (2002) Topology optimization of compliant mechanisms using evolutionary algorithm with design geometry encoded as a graph. Presented at the 2002 ASME Design Engineering Technical Conferences, Montreal, Canada, September 29–October 2, 2002, paper no. DETC2002/DAC-34147

  2. Atrek E (1989) SHAPE: A program for shape optimization of continuum structures. In: Brebbia CA, Hernandez S (eds) Computer aided optimum design of structures: applications. Southampton, Computational Mechanics, pp 135–144

  3. Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197–224

    Google Scholar 

  4. Chapman CD, Jakiela MJ (1996) Genetic algorithm-based structural topology design with compliance and topology simplification considerations. ASME J Mech Des 118:89–98

    Google Scholar 

  5. Chapman CD, Saitou K, Jakiela MJ (1994) Genetic algorithms as an approach to configuration and topology design. ASME J Mech Des 116:1005–1012

    Google Scholar 

  6. Cui GY, Tai K, Wang BP (2002) Topology optimization for maximum natural frequency using simulated annealing and morphological representation. AIAA J 40(3):586–589

    Google Scholar 

  7. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, Chichester

  8. Frecker MI, Ananthasuresh GK, Nishiwaki S, Kikuchi N, Kota S (1997) Topological synthesis of compliant mechanisms using multi-criteria optimization. ASME J Mech Des 119:238–245

    Google Scholar 

  9. Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading, Massachusetts

  10. Gross J, Yellen J (1999) Graph theory and its applications. CRC, Boca Raton

  11. Hamda H, Jouve F, Lutton E, Schoenauer M, Sebag M (2002) Compact unstructured representations for evolutionary design. Appl Int 16(2):139–155

    Google Scholar 

  12. Hetrick JA, Kota S (1999) An energy formulation for parametric size and shape optimization of compliant mechanisms. ASME J Mech Des 121:229–234

    Google Scholar 

  13. Howell LL (2001) Compliant mechanisms. Wiley, New York

  14. Jakiela MJ, Chapman C, Duda J, Adewuya A, Saitou K (2000) Continuum structural topology design with genetic algorithms. Comput Methods Appl Mech Eng 186(2–4):339–356

    Google Scholar 

  15. Kane C, Schoenauer M (1996) Topological optimum design using genetic algorithms. Control Cybern 25(5):1059–1088

    Google Scholar 

  16. Larsen UD, Sigmund O, Bouwstra S (1997) Design and fabrication of compliant micromechanisms and structures with negative Poisson’s ratio. J Microelectromech Syst 6:99–106

    Google Scholar 

  17. Liu JS, Parks GT, Clarkson PJ (2000) Metamorphic development: a new topology optimization method for continuum structures. Struct Multidisc Optim 20:288–300

    Google Scholar 

  18. Mortenson ME (1997) Geometric modeling, 2nd edn. Wiley, New York

  19. Parsons R, Canfield SL (2002) Developing genetic programming techniques for the design of compliant mechanisms. Struct Multidisc Optim 24:78–86

    Google Scholar 

  20. Pedersen CBW, Buhl T, Sigmund O (2001) Topology synthesis of large-displacement compliant mechanisms. Int J Numer Methods Eng 50:2683–2705

    Google Scholar 

  21. Ray T, Tai K, Seow KC (2001) Multiobjective design optimization by an evolutionary algorithm. Eng Optim 33:399–424

    Google Scholar 

  22. Rozvany GIN (1981) Optimality criteria for grids, shells and arches. in: haug ej, cea J (eds.) Optimization of distributed parameter structures: vol. 1—Proceedings of the NATO Advanced Study Institute, Sijthoff & Noordhoff, Alphen aan den Rijn (the Netherlands), pp 112–151

  23. Rozvany GIN (2001a) Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics. Struct Optim 21:90–108

    Google Scholar 

  24. Rozvany GIN (2001b) Stress ratio and compliance based methods in topology optimization—a critical review. Struct Optim 21:109–119

    Google Scholar 

  25. Rozvany GIN, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Struct Optim 4:250–254

    Google Scholar 

  26. Russell DM, Manoochehri SP (1989) A two dimensional rule-based shape synthesis method. In: Ravani B (ed.) Advances in design automation, 1989, Vol. 2, Design Optimization. ASME, New York, pp 217–223

  27. Saxena A, Ananthasuresh GK (2001) Topology synthesis of compliant mechanisms for nonlinear force-deflection and curved path specifications. ASME J Mech Des 123:33–42

    Google Scholar 

  28. Schoenauer M (1995) Shape representation for evolutionary optimization and identifcation in structural mechanics. In: Winter G, Periaux J, Galan M, Cuesta P (eds.) Genetic Algorithms in engineering and computer science. Wiley, Chichester, pp 443–464

  29. Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Mach 25:493–524

    Google Scholar 

  30. Sigmund O (2001) A 99 line topology optimization code written in MATLAB. Struct Multidisc Optim 21(2):120–127

    Google Scholar 

  31. Soto CA (2001) Structural topology optimization: from minimizing compliance to maximizing energy absorption. Int J Vehicle Des 25(1/2):142–163

    Google Scholar 

  32. Tai K, Chee TH (1998) Genetic algorithm with structural morphology representation for topology design optimization. In: Gentle CR, Hull JB (eds.) Mechanics in design—Proceedings of the 2nd international conference on mechanics in design, Nottingham, pp 827–836

  33. Tai K, Chee TH (2000) Design of structures and compliant mechanisms by evolutionary optimization of morphological representations of topology. ASME J Mech Des 122:560–566

    Google Scholar 

  34. Tai K, Cui GY, Ray T (2002) Design synthesis of path generating compliant mechanisms by evolutionary optimization of topology and shape. ASME J Mech Des 124(3):492–500

    Google Scholar 

  35. Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49:885–896

    Google Scholar 

  36. Yang RJ, Chuang CH (1994) Optimal topology design using linear programming. Comput Struct 52:265–275

    Google Scholar 

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Authors and Affiliations

  1. Centre for Advanced Numerical Engineering Simulations, School of Mechanical and Production Engineering, Nanyang Technological University, 50 Nanyang Ave, Singapore, 639798, Singapore

    K. Tai & S. Akhtar

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  1. K. Tai
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  2. S. Akhtar
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Correspondence to K. Tai.

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Tai, K., Akhtar, S. Structural topology optimization using a genetic algorithm with a morphological geometric representation scheme. Struct Multidisc Optim 30, 113–127 (2005). https://doi.org/10.1007/s00158-004-0504-y

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  • DOI: https://doi.org/10.1007/s00158-004-0504-y

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