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Three-dimensional polyhedral reciprocal diagrams

This research extends reciprocal form and force diagrams to spatial structures, develops algorithms to control these dependent geometrical representations to steer structural form, and demonstrates the new design possibilities of the new structural design framework.

More info

This research develops a three-dimensional extension of graphic statics, based on polyhedral form and force diagrams, for compression-only and tension-only spatial structures with externally applied loads. It illustrates and clarifies Rankine's original proposition about the equilibrium of spatial frames and Maxwell's procedures for geometrically constructing three-dimensional reciprocal diagrams in specific cases. An updated definition for polyhedral, reciprocal form and force diagrams that allows including external forces is established. The computational procedure for constructing the form diagram from a given force diagram is presented and described. With an implementation of the presented approach in a CAD environment, for example, branching structures, spatial frames, and cellular structures can be designed based on chosen force distributions.

Publications

Akbarzadeh M.Three-dimensional Graphical Statics using Polyhedral Reciprocal Diagrams,ETH Zurich, Department of ArchitectureZurich,2016 (October).
Akbarzadeh M., Van Mele T. and Block P.On the Equilibrium of Funicular Polyhedral Frames and Convex Polyhedral Force Diagrams,Computer-Aided Design,63: 118-128,2015.
Akbarzadeh M., Van Mele T. and Block P.Three-dimensional Graphic Statics: Initial explorations with polyhedral form and force diagrams,International Journal of Space Structures,31(2): 217-226,2016 (June).
Akbarzadeh M., Van Mele T. and Block P.Equilibrium of spatial networks using 3D reciprocal diagrams,Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2013,Obrębski, J.B. and Tarczewski, R. (editors),Wroclaw, Poland,2013 (September).
Akbarzadeh M., Van Mele T. and Block P.Spatial compression-only form finding through subdivision of external force polyhedron,Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium,Amsterdam,2015 (August).
Akbarzadeh M., Van Mele T. and Block P.3D Graphic Statics: Geometric Construction of Global Equilibrium,Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium,Amsterdam,2015 (August).
Akbarzadeh M., Van Mele T. and Block P.Compression-only form finding through finite subdivision of the external force polygon,Proceedings of the IASS-SLTE 2014 Symposium,Brasilia, Brazil,2014.
ETH ZurichDARCHITA

 

ETH Zurich
Institute of Technology in Architecture
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