Skip to main content
SpringerLink
Log in

Optimising the load path of compression-only thrust networks through independent sets

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

This paper presents network load path optimisation for the weight minimisation of compression-only thrust networks, allowing for the design of material efficient surface structures. A hybrid evolutionary and function-gradient optimisation process finds the optimal internal force state of the network, by manipulating the force densities of a selected number of edges based on the network indeterminacy. These selected edges are the independent sets, and are found through the Reduced Row Echelon form of the network’s equilibrium matrix. It was found that networks can have certain independent sets that have a significant influence on both the stability of the optimisation algorithm, and in the final load path/volume of the structure. Finding the most effective independent sets was handled by data-driven methods, applied to many thousands of independent set trials. This provided insight into the behaviour of the underlying network and dramatically increased the rate of finding successful independent sets. The importance and weights of the network edges highlighted key areas of the network that allowed structural judgement and improvements to be made.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  • Baker WF, Beghini LL, Mazurek A, Carrion J, Beghini A (2013) Maxwell’s reciprocal diagrams and discrete Michell frames. Struct Multidiscip Optim 48(2):267–277

    Article  MathSciNet  Google Scholar 

  • Beghini LL, Carrion J, Beghini A, Mazurek A, Baker WF (2014) Structural optimization using graphic statics. Struct Multidiscip Optim 49(3):351–366

    Article  Google Scholar 

  • Block P, Ochsendorf J (2007) Thrust network analysis: a new methodology for three-dimensional equilibrium. J Int Assoc Shell Spatial Struct 48(3):167–173

    Google Scholar 

  • Block P (2009) Thrust Network Analysis: Exploring three-dimensional equilibrium. PhD dissertation, Massachusetts Institute of Technology, Cambridge

  • Block P, Lachauer L (2014) Three-dimensional funicular analysis of masonry vaults. Mechan Res Commun 56:53–60

    Article  Google Scholar 

  • Block Research Group (2014) ETH Zurich, RhinoVAULT - Designing funicular form with Rhino. [Online] Available at http://block.arch.ethz.ch/brg/tools/rhinovault

  • Breiman L (2001) Random forests. Mach Learn 45(1):5–32

    Article  MATH  Google Scholar 

  • De Wilde WP (2006) Conceptual design of lightweight structures: the role of morphological indicators and the structural index. High Perform Struct Mater III: WIT Trans Built Environ 85:3–12

    Google Scholar 

  • Pedregosa, et al. (2011) Scikit-learn: machine learning in Python. JMLR 12:2825–2830

    MathSciNet  MATH  Google Scholar 

  • Python Software Foundation (2017) Python Language Reference. Version 3.6

  • Fraternali F (2010) A thrust network approach to the equilibrium problem of unreinforced masonry vaults via polyhedral stress functions. Mechan Res Commun 37:198–204

    Article  MATH  Google Scholar 

  • Gilbert M, Tyas A (2003) Layout optimization of large-scale pin-jointed frames. Eng Comput 20(8):1044–1064

    Article  MATH  Google Scholar 

  • Goldberg DE (1989) Genetic algorithms in search, optimization & machine learning, 1st edn. Addison-Wesley Professional, Boston

    MATH  Google Scholar 

  • He L, Gilbert M (2015) Rationalization of trusses generated via layout optimization. Struct Multidiscip Optim 52(4):677–694

    Article  MathSciNet  Google Scholar 

  • Holland JH (1975) Adaptation in natural and artificial systems, 1st edn. The University of Michigan, Ann Arbor

    Google Scholar 

  • Jiang Y, Zegard T, Baker WF (2018) Form-finding of grid-shells using the ground structure and potential energy methods: a comparative study and assessment. Struct Multidiscip Optim 57:1187–1211

    Article  Google Scholar 

  • Jones E, Oliphant T, Peterson P et al (2001) SciPy: Open source scientific tools for Python. [Online; accessed 2017-02-13]

  • Liew A, Pagonakis D, Van Mele T, Block P (2018) Load-path optimisation of funicular networks. Meccanica 53:279–294

    Article  MathSciNet  MATH  Google Scholar 

  • Linkwitz K, Schek HJ (1971) Einige Bemerkungen zur Berechnung von vorgespannten Seilnetzkonstruktionen. Ingenieur – Archiv 40:145–158

    Article  Google Scholar 

  • Lu H, Gilbert M, Tyas A (2018) Theoretically optimal bracing for pre-existing building frames. Struct Multidiscip Optim 58(2):677–686

    Article  Google Scholar 

  • Marmo F, Rosati L (2017) Reformulation and extension of the thrust network analysis. Comput Struct 182:104–118

    Article  Google Scholar 

  • Maxwell JC (1864) On reciprocal figures and diagrams of forces. Philos Mag J Ser 4(27):250–261

    Article  Google Scholar 

  • Mazurek A, Baker WF, Tort C (2011) Geometrical aspects of optimum truss like structures. Struct Multidiscip Optim 43(2):231–242

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • O’Dwyer DW (1999) Funicular analysis of masonry vaults. Comput Struct 73:187–197

    Article  MATH  Google Scholar 

  • Pyl L, Sitters CWM, De Wilde WP (2013) Design and optimization of roof trusses using morphological indicators. Adv Eng Softw 62-63:9–19

    Article  Google Scholar 

  • Schek HJ (1974) The force density method for form finding and computation of general networks. Comput Methods Appl Mech Eng 3:115–134

    Article  MathSciNet  Google Scholar 

  • Storn R, Price K (1997) Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    Article  MathSciNet  MATH  Google Scholar 

  • Stromberg LL, Beghini A, Baker WF, Paulino GH (2018) Topology optimization for braced frames: combining continuum and beam/column elements. Eng Struct 37:106–124

    Article  Google Scholar 

  • TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015) Version 1.7.0. Online: https://www.tensorflow.org

  • Van der Walt S, Colbert C, Varoquaux G (2011) The NumPy array: A structure for efficient numerical computation. Comput Sci Eng 13:22–30

    Article  Google Scholar 

  • Van Mele T, Block P (2014) Algebraic graph statics. Comput-Aided Des 53:104–116

    Article  Google Scholar 

  • Van Mele T, Liew A, Mendéz T, Rippmann M et al (2017) COMPAS: A framework for computational research in architecture and structures. [Online; accessed 2017-07-06]

  • Vandenbergh T, De Wilde WP, Latteur P, Verbeeck B, Ponsaert1 W, Van Steirteghem J (2006) Influence of stiffness constraints on optimal design of trusses using morphological indicators. High Perform Struct Mater III: WIT Trans Built Environ 85:31–40

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Technology in Architecture, ETH Zurich, Stefano-Franscini-Platz 1, 8093, Zurich, Switzerland

    A. Liew, R. Avelino, V. Moosavi, T. Van Mele & P. Block

Authors
  1. A. Liew
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Avelino
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. Moosavi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. T. Van Mele
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. P. Block
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Liew.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Responsible Editor: Somanath Nagendra

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liew, A., Avelino, R., Moosavi, V. et al. Optimising the load path of compression-only thrust networks through independent sets. Struct Multidisc Optim 60, 231–244 (2019). https://doi.org/10.1007/s00158-019-02214-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-019-02214-w

Keywords

Search

Navigation