Area-controlled construction of global force polyhedra

Lee J., Van Mele T. and Block P.
Proceedings of the IASS Symposium 2017

This paper presents an interactive algorithm for constructing force polyhedra used in three-dimensional graphic statics with pre-defined or target force magnitudes. It has been shown how force polyhedra can be geometrically constructed to describe the static equilibrium of spatial structures, where the areas and normals of the faces of the force polyhedra represent the magnitudes and directions of the corresponding forces in the structure, respectively. However, controlling the geometry of force polyhedra with face area constraints (or equivalently, force magnitude constraints), has yet to be investigated in detail. While the mathematical formulation of polyhedra is a well-studied topic in discrete and computational geometry, previous work from these fields are concerned more with improving the efficiency and purity of the iterative optimization procedures that find absolute solutions, than exploring the diversity of possible solutions, which is more important within the contexts of architecture and structural design.

This paper implements the latest research in construction of polyhedra with face area constraints from various fields in a CAD environment, which allows designers to easily incorporate unknown design variables and various indeterminacies of the boundary conditions to explore a wide range of possible equilibrium solutions. Several key examples will demonstrate practical applications of the presented algorithm in enabling force polyhedra used in three-dimensional graphic statics to be a viable tool during early stages of design not just for form-finding explorations, but also for addressing more precise, quantitative boundary condition criteria.


    author    = "Lee, J. and Van Mele, T. and Block, P.",
    title     = "Area-controlled construction of global force polyhedra",
    booktitle = "Proceedings of the IASS Symposium 2017",
    year      = "2017",
    editor    = "",
    volume    = "",
    number    = "",
    pages     = "",
    publisher = "",
    address   = "Hamburg",
    month     = "September",
    doi       = "",
    note      = "",

Related publications

Lee J., Van Mele T. and Block P.Form-finding explorations through geometric manipulations of force polyhedrons,Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2016,Tokyo, Japan,2016 (September).
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.On the Equilibrium of Funicular Polyhedral Frames and Convex Polyhedral Force Diagrams,Computer-Aided Design,63: 118-128,2015.


ETH Zurich
Institute of Technology in Architecture
Block Research Group
Stefano-Franscini-Platz 1, HIB E 45
8093 Zurich, Switzerland

+41 44 633 38 35  phone
+41 44 633 10 53  fax

Copyright © 2009-2024 Block Research Group, ETH Zurich, Switzerland.