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Design of conjugate, conjoined shapes and tilings using topology optimization

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Abstract

We present a method for obtaining conjugate, conjoined shapes and tilings in the context of the design of structures using topology optimization. Optimal material distribution is achieved in topology optimization by setting up a selection field in the design domain to determine the presence/absence of material there. We generalize this approach in this paper by presenting a paradigm in which the material left out by the selection field is also utilised. We obtain conjugate shapes when the region chosen and the region left-out are solutions for two problems, each with a different functionality. On the other hand, if the left-out region is connected to the selected region in some pre-determined fashion for achieving a single functionality, then we get conjoined shapes. The utilization of the left-out material, gives the notion of material economy in both cases. Thus, material wastage is avoided in the practical realization of these designs using many manufacturing techniques. This is in contrast to the wastage of left-out material during manufacture of traditional topology-optimized designs. We illustrate such shapes in the case of stiff structures and compliant mechanisms. When such designs are suitably made on domains of the unit cell of a tiling, this leads to the formation of new tilings which are functionally useful. Such shapes are not only useful for their functionality and economy of material and manufacturing, but also for their aesthetic value.

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References

  • Alwan A, Ananthasuresh GK (2006) Coupled electrostatic-elastic analysis for topology optimization using material interpolation. In: International MEMS conference, Journal of Physics: conference series, vol 34, pp 264–270

  • Balaji G, Biradar P, Saikrishna C, Venkata Ramaiah K, Bhaumik S, Haruray A, Ananthasuresh GK (2008) An SMA-actuated, compliant mechanism-based pipe-crawler. In: International conference on smart materials, structures, and systems

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

    Article  Google Scholar 

  • Bendsøe MP, Sigmund O (2003) Topology optimization—theory methods and applications, vol 4, 2nd edn. Springer, Berlin

    Google Scholar 

  • Borrvall T, Petersson J (2003) Topology optimization of fluids in stokes flow. Int J Numer Methods Fluids 41:77–107

    Article  MATH  MathSciNet  Google Scholar 

  • Deepak RS, Mana D, Sahu D, Ananthasuresh GK et al (2009) A comparative study of the formulations and benchmark problems for topology optimization of compliant mechanisms. J Mech Robot 1:011003

    Article  Google Scholar 

  • Diaz A, Bendsøe MP (1992) Shape optimization of structures for multiple loading conditions using a homogenization method. Struct Optim 4:17–22

    Article  Google Scholar 

  • Evgrafov A, Pingen G, Maute K et al (2006) Topology optimization of fluid problems by the lattice boltzmann method. In: IUTAM symposium on topological design optimization of structures, machines and materials: status and perspectives. Springer, pp 559–568

    Chapter  Google Scholar 

  • Knowles PR (1991) Castellated beams. In: Structural and building board, vol 90, pp 521–536

  • Limaye P, Meenakshi Sundaram M, Ananthasuresh GK (2009) Optimal conjugate topologies on a single domain. In: 8th world congress on structural optimization, Lisbon, Portugal

  • Pedersen CG, Lund JJ, Damkilde L, Kristensen AS et al (2006) Topology optimization—improved checker-board filtering with sharp contours. In: 19th Nordic seminar on computational mechanics, p 4

  • Raulli M, Maute K (2005) Topology optimization of electrostatically actuated microsystems. Struct Multidisc Optim 30(5):342–359

    Article  Google Scholar 

  • Roach G, Howell L (2002) Evaluation and comparison of alternative compliant overrunning clutch designs. J Mech Des 124:485–491

    Article  Google Scholar 

  • Saxena A, Ananthasuresh GK (2000) On an optimal property of compliant topologies. Struct Multidisc Optim 19:36–49

    Article  Google Scholar 

  • Sigmund O (2001) Topology optimization methods with applications in mechanisms, MEMS and material design. Solid Mechanics, Department of Mechanical Engineering, Technical University of Denmark

  • Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidisc Optim 33:401–424

    Article  Google Scholar 

  • Sigmund O, Clausen PM (2007) Topology optimization using a mixed formulation: an alternative way to solve pressure load problems. Comput Methods Appl Mech Eng 196:1874–1889

    Article  MATH  MathSciNet  Google Scholar 

  • Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24:359–373

    Article  MATH  MathSciNet  Google Scholar 

  • Wang M, Wang S (2005) Bilateral filtering for structural topology optimization. Int J Numer Methods Eng 63(13):1911–1938

    Article  MATH  Google Scholar 

  • Yin L, Ananthasuresh GK (2001) Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme. Struct Multidisc Optim 23:49–62

    Article  Google Scholar 

  • Yin L, Ananthasuresh GK (2003) Design of distributed compliant mechanisms. Mech Based Des Struct Mach 31(2):151–179

    Article  Google Scholar 

  • Yoon GH, Sigmund O (2008) A monolithic approach for topology optimization of electrostatically actuated devices. Comput Methods Appl Mech Eng 197:4062–4075

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to thank G. Ramu and M.S. Deepika for his help in manufacturing the prototypes. Anonymous reviewers’ comments on improving the organisation of the paper are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India

    M. Meenakshi Sundaram, Padmanabh Limaye & G. K. Ananthasuresh

Authors
  1. M. Meenakshi Sundaram
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  2. Padmanabh Limaye
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  3. G. K. Ananthasuresh
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Corresponding author

Correspondence to M. Meenakshi Sundaram.

Additional information

An enhanced version of a brief conference paper presented at the World Conference of Structural and Multi-disciplinary Optimization 2009, titled ‘Optimal conjugate topologies on a single domain’, by Padmanabh Limaye, M. Meenakshi Sundaram, and G. K. Ananthasuresh.

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Sundaram, M.M., Limaye, P. & Ananthasuresh, G.K. Design of conjugate, conjoined shapes and tilings using topology optimization. Struct Multidisc Optim 45, 65–81 (2012). https://doi.org/10.1007/s00158-011-0657-4

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  • DOI: https://doi.org/10.1007/s00158-011-0657-4

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