Optimising the load path of compression-only thrust networks through independent sets
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.
KeywordsReduced Row Echelon Equilibrium matrix Optimisation algorithm
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
- Block P, Ochsendorf J (2007) Thrust network analysis: a new methodology for three-dimensional equilibrium. J Int Assoc Shell Spatial Struct 48(3):167–173Google Scholar
- Block P (2009) Thrust Network Analysis: Exploring three-dimensional equilibrium. PhD dissertation, Massachusetts Institute of Technology, CambridgeGoogle Scholar
- Block Research Group (2014) ETH Zurich, RhinoVAULT - Designing funicular form with Rhino. [Online] Available at http://block.arch.ethz.ch/brg/tools/rhinovault
- 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 85:3–12Google Scholar
- Python Software Foundation (2017) Python Language Reference. Version 3.6Google Scholar
- Holland JH (1975) Adaptation in natural and artificial systems, 1st edn. The University of Michigan, Ann ArborGoogle Scholar
- Jones E, Oliphant T, Peterson P et al (2001) SciPy: Open source scientific tools for Python. [Online; accessed 2017-02-13]Google Scholar
- TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015) Version 1.7.0. Online: https://www.tensorflow.org
- 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]Google Scholar
- 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 85:31–40Google Scholar