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Advanced Topology Optimization Methods for Conceptual Architectural Design

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Advances in Architectural Geometry 2014

Abstract

This paper presents a series of new, advanced topology optimization methods, developed specifically for conceptual architectural design of structures. The proposed computational procedures are implemented as components in the framework of a Grasshopper plugin, providing novel capacities in topological optimization: Interactive control and continuous visualization; embedding flexible voids within the design space; consideration of distinct tension / compression properties; and optimization of dual material systems. In extension, optimization procedures for skeletal structures such as trusses and frames are implemented. The developed procedures allow for the exploration of new territories in optimization of architectural structures, and offer new methodological strategies for bridging conceptual gaps between optimization and architectural practice.

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References

  • Aage, N., Lazarov, B.S.: Parallel framework for topology optimization using the method of moving asymptotes. Struct. Multidiscip. Optim. 47(4), 493–505 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  • Aage, N., Nobel-Jørgensen, M., Andreasen, C.S., Sigmund, O.: Interactive topology optimization on hand-held devices. Struct. Multidiscip. Optim. 47(1), 1–6 (2013)

    Article  Google Scholar 

  • Amir, O.: A topology optimization procedure for reinforced concrete structures. Comput. Struct. 114, 46–58 (2013)

    Article  Google Scholar 

  • Amir, O., Sigmund, O.: Reinforcement layout design for concrete structures based on continuum damage and truss topology optimization. Struct. Multidiscip. Optim. 47, 157–174 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  • Amir, O., Aage, N., Lazarov, B.S.: On multigrid-CG for efficient topology optimization. Struct. Multidiscip. Optim. 48, 815–829 (2014)

    Article  MathSciNet  Google Scholar 

  • Andreassen, E., Clausen, A., Schevenels, M., Lazarov, B.S., Sigmund, O.: Efficient topology optimization in MATLAB using 88 lines of code. Struct. Multidiscip. Optim. 43(1), 1–16 (2011)

    Article  MATH  Google Scholar 

  • Beghini, A., Beghini, L., Baker, W.: Applications of structural optimization in architectural design. Struct. Congress 2013, 2499–2507 (2013)

    Google Scholar 

  • Bendsøe, M.P.: Optimal shape design as a material distribution problem. Struct. Optim. 1, 193–202 (1989)

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Bendsøe, M.P., Sigmund, O.: Topology Optimization – Theory, Methods and Applications. Springer, Berlin/New York (2003)

    Google Scholar 

  • Besserud, K., Katz, N., Beghini, A.: Structural emergence: architectural and structural design collaboration at SOM. Archit. Des. 83(2), 48–55 (2013)

    Google Scholar 

  • Bogomolny, M., Amir, O.: Conceptual design of reinforced concrete structures using topology optimization with elasto-plastic material modeling. Int. J. Numer. Meth. Eng. 90, 1578–1597 (2012)

    Article  MATH  Google Scholar 

  • Borel, P.I., Harpøth, A., Frandsen, L., Kristensen, M., Shi, P., Jensen, J., Sigmund, O.: Topology optimization and fabrication of photonic crystal structures. Opt. Express 12(9), 1996–2001 (2004)

    Article  Google Scholar 

  • Buswell, R.A., Soar, R.C., Gibb, A.G.F., Thorpe, A.: Freeform construction: mega-scalerapid manufacturing for construction. Autom. Constr. 16, 224–231 (2007)

    Article  Google Scholar 

  • Cai, K.: A simple approach to find optimal topology of a continuum with tension-only or compression-only material. Struct. Multidiscip. Optim. 43(6), 827–835 (2011)

    Article  Google Scholar 

  • Clausen, A., Aage, N., Sigmund, O.: Topology optimization with flexible void area. Struct. Multidiscip. Optim. (2014, in press)

    Google Scholar 

  • Davis, T.A.: Direct Methods for Sparse Linear Systems. SIAM, Philadelphia (2006)

    Book  MATH  Google Scholar 

  • Dombernowsky, P., Søndergaard, A.: Unikabeton prototype. In: Fabricate: Making Digital Architecture. Riverside Architectural Press, Toronto (2011)

    Google Scholar 

  • Dombernowsky, P., Søndergaard, A.: Design, analysis and realization of topology optimized concrete structures. Int. Assoc. Shell Spat. Struct. 53, 209–216 (2012)

    Google Scholar 

  • Dorn, W.S., Gomory, R.E., Greenberg, H.J.: Automatic design of optimal structures. J. Mecanique 3(1), 25–52 (1964)

    Google Scholar 

  • Frattari, L.: The structural from: topology optimization in architecture and industrial design. Doctoral dissertation, School of Advanced Studies, University of Camerino (2011)

    Google Scholar 

  • Hemp, W.S.: Optimum structures. Clarendon, Oxford (1973)

    Google Scholar 

  • Huang, X., **e, Y.M.: Evolutionary Topology Optimization of Continuum Structures: Methods and Applications. Wiley, Chichester (2010). 235 pp. ISBN 9780470746530

    Book  Google Scholar 

  • Jonsmann, J., Sigmund, O., Bouwstra, S.: Compliant electro-thermal microactuators. In: Micro Electro Mechanical Systems, pp. 588–593. IEEE (1999)

    Google Scholar 

  • Kato, J., Ramm, E.: Optimization of fiber geometry for fiber reinforced composites considering damage. Finite Elem. Anal. Des. 46, 401–415 (2010)

    Article  Google Scholar 

  • Kato, J., Lipka, A., Ramm, E.: Multiphase material optimization for fiber reinforced composites with strain softening. Struct. Multidiscip. Optim. 39, 63–81 (2009)

    Article  Google Scholar 

  • Kirsch, U.: Structural Optimization. Springer, Berlin/New York (1993)

    Book  Google Scholar 

  • Le, T., Austin, S.: High-performance printing concrete for freeform building components. In: Proceedings of the FIB Symposium, PRAGUE 2011 (2011)

    Google Scholar 

  • Liu, S., Qiao, H.: Topology optimization of continuum structures with different tensile and compressive properties in bridge layout design. Struct. Multidiscip. Optim. 43(3), 369–380 (2011)

    Article  MathSciNet  Google Scholar 

  • Martinez, P., Marti, P., Querin, O.M.: Growth method for size, topology, and geometry optimization of truss structures. Struct. Multidiscip. Optim. 33(1), 13–26 (2007)

    Article  Google Scholar 

  • Michell, A.G.M.: The limits of economy of material in frame-structures. Lond. Edinb. Dublin Philos. Mag. J. Sci. 8(47), 589–597 (1904)

    Article  MATH  Google Scholar 

  • Mostafavi, S., Beltran, M. M., Biloria, N.: Performance Driven Design and Design Information Exchange (2013)

    Google Scholar 

  • Park, P., Gilbert, M., Tyas, A., Popovic-Larsen, O.: Potential use of structural layout optimization at the conceptual design stage. Int. J. Archit. Comput. 10, 13–32 (2012)

    Article  Google Scholar 

  • Pedersen, P.: On optimal orientation of orthotropic materials. Struct. Optim. 1(2), 101–106 (1989)

    Article  Google Scholar 

  • Rozvany, G.I.: Optimal Design of Flexural Systems: Beams, Grillages, Slabs, Plates, and Shells. Pergamon Press, Oxford/New York (1976)

    Google Scholar 

  • Sardan, O., Eichhorn, V., Petersen, D.H., Fatikow, S., Sigmund, O., Bøggild, P.: Rapid prototy** of nanotube-based devices using topology-optimized microgrippers. Nanotechnology 19(49), 495–503 (2008)

    Article  Google Scholar 

  • Sasaki, M., Itō, T., Isozaki, A.: Morphogenesis of Flux Structure. AA Publications, London (2007)

    Google Scholar 

  • Sigmund, O.: A 99 line topology optimization code written in Matlab. Struct. Multidiscip. Optim. 21(2), 120–127 (2001)

    Article  Google Scholar 

  • Sigmund, O., Bendsøe, M.P.: Topology optimization: from airplanes to nano-optics. In: Stubkjær, K., Kortenbach, T. (eds.) Bridging From Technology to Society. Technical University of Denmark, Lyngby (2004)

    Google Scholar 

  • Sigmund, O., Jensen, J.S.: Systematic design of phononic band–gap materials and structures by topology optimization. Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci. 361(1806), 1001–1019 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  • Sigmund, O., Torquato, S.: Design of materials with extreme thermal expansion using a three-phase topology optimization method. J. Mech. Phys. Solids 45(6), 1037–1067 (1997)

    Article  MathSciNet  Google Scholar 

  • Søndergaard, A., Feringa, J.: An integral approach to structural optimization and fabrication. In: Acadia, 491–497 (2014)

    Google Scholar 

  • Søndergaard, A., Amir, O., Knauss, M.: Topology optimization and digital assembly of advanced space-frame structures. In: 2013 ACADIA Conference (2013)

    Google Scholar 

  • Stromberg, L.L., Beghini, A., Baker, W.F., Paulino, G.H.: Topology optimization for braced frames: combining continuum and beam/column elements. Eng. Struct. 37, 106–124 (2012)

    Article  Google Scholar 

  • The Mathworks.: MATLAB version 8.1.0.604 (R2013a) (2013)

    Google Scholar 

  • Victoria, M., Querin, O.M., Martí, P.: Generation of strut-and-tie models by topology optimization using different material properties in tension and compression. Struct. Multidiscip. Optim. 44, 247–258 (2011)

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank Ole Sigmund for plenty of fruitful discussions and suggestions, and for his active support in the development of the TopOpt plugin. Financial support for the second author, received from the European Commission Research Executive Agency, grant agreement PCIG12-GA-2012-333647, is gratefully acknowledged.

Author information

Authors and Affiliations

  1. DTU – Technical University of Denmark, Kongens Lyngby, Denmark

    Niels Aage & Anders Clausen

  2. Technion – Israel Institute of Technology, Haifa, Israel

    Oded Amir & Lior Hadar

  3. Aarhus School of Architecture, Aarhus, Denmark

    Dana Maier & Asbjørn Søndergaard

Authors
  1. Niels Aage
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  2. Oded Amir
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  3. Anders Clausen
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  4. Lior Hadar
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  5. Dana Maier
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  6. Asbjørn Søndergaard
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Corresponding author

Correspondence to Niels Aage .

Editor information

Editors and Affiliations

  1. BLOCK Research Group, ETH Zürich, Institute for Technology in Architecture, Zürich, Switzerland

    Philippe Block

  2. University of Stuttgart, Inst. of Building Structures and Structural Design, Stuttgart, Germany

    Jan Knippers

  3. University College London, Dept. of Computer Science, London, United Kingdom

    Niloy J. Mitra

  4. The University of Hong Kong, Dept. of Computer Science, Hong Kong, Hong Kong SAR

    Wen** Wang

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Aage, N., Amir, O., Clausen, A., Hadar, L., Maier, D., Søndergaard, A. (2015). Advanced Topology Optimization Methods for Conceptual Architectural Design. In: Block, P., Knippers, J., Mitra, N., Wang, W. (eds) Advances in Architectural Geometry 2014. Springer, Cham. https://doi.org/10.1007/978-3-319-11418-7_11

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