On the equilibrium of funicular polyhedral frames and convex polyhedral force diagrams

Akbarzadeh, Masoud; Mele, Tom Van; Block, Philippe

doi:10.1016/j.cad.2015.01.006

Cited by 75 publications

(52 citation statements)

References 10 publications

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“…The polyhedron-based approach, initially introduced by Rankine (1864) and later developed by Maxwell (1867), considers a force diagram built as an assembly of force polyhedral cells ( Figure 1b) with areas equivalent to force magnitudes. General procedures to construct and manipulate polyhedron-based form and force diagrams have been developed only recently (Akbarzadeh et al 2015;Lee et al, 2018;Konstantatou et al, 2018).…”

Section: Graphic Statics In 3dmentioning

confidence: 99%

Vector-based 3D graphic statics: A framework for the design of spatial structures based on the relation between form and forces

D’Acunto

Jasienski

Ohlbrock

et al. 2019

International Journal of Solids and Structures

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This article develops a vector-based 3D graphic statics framework that uses synthetic and intuitive graphical means for the analysis and design of spatial structures such as networks of bar elements in static equilibrium. It is intended to support the collaborative work of structural engineers and architects from the conceptual phase of the design process. Several procedures for the construction of a vector-based 3D force diagram for any given 3D form diagram with an underlying planar or non-planar graph are identified and described. In the non-planar case, the proposed procedures rely on the preliminary topological planarization of the graph by cutting the crossing edges and reconnecting them to one or more newly inserted auxiliary vertices. The resulting planar graph can be then used as a base for the assembly of the 3D force diagram, without altering the static equilibrium of the structure. An implementation of the proposed framework to real design scenarios is presented through two case studies. These examples show how to take advantage of the bi-directional manipulation of the diagrams in the structural design process.

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Section: Graphic Statics In 3dmentioning

confidence: 99%

Vector-based 3D graphic statics: A framework for the design of spatial structures based on the relation between form and forces

D’Acunto

Jasienski

Ohlbrock

et al. 2019

International Journal of Solids and Structures

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“…The first step in the computational setup is to define the topology of the primal complex including the cells, edges and faces and construct their connectivity matrices. Winged-Edge data structure (WED) or alike can be used to find all possible convex cells and the topological relationships [5,7]. One of the current limitations of this implementation is that the input cannot accept complex (self-intersecting) faces, and therefore, it can only find convex polyhedral cells.…”

Section: Constructing the Winged-edge Data Structurementioning

confidence: 99%

Algebraic 3D graphic statics: Reciprocal constructions

Hablicsek

Akbarzadeh

Guo

2019

Computer-Aided Design

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The recently developed 3D graphic statics (3DGS) lacks a rigorous mathematical definition relating the geometrical and topological properties of the reciprocal polyhedral diagrams as well as a precise method for the geometric construction of these diagrams. This paper provides a fundamental algebraic formulation for 3DGS by developing equilibrium equations around the edges of the primal diagram and satisfying the equations by the closeness of the polygons constructed by the edges of the corresponding faces in the dual/reciprocal diagram. The research provides multiple numerical methods for solving the equilibrium equations and explains the advantage of using each technique. The approach of this paper can be used for compression-and-tension combined form-finding and analysis as it allows constructing both the form and force diagram based on the interpretation of the input diagram. Besides, the paper expands on the geometric/static degrees of (in)determinacies of the diagrams using the algebraic formulation and shows how these properties can be used for the constrained manipulation of the polyhedrons in an interactive environment without breaking the reciprocity between the two. Keywords: Algebraic three-dimensional graphic statics, polyhedral reciprocal diagrams, geometric degrees of freedom, static degrees of indeterminacies, tension and compression combined polyhedra, constraint manipulation of polyhedral diagrams.

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“…Achieving stability through geometry rather than material strength opens up the possibility of using weak materials in structural applications. The geometry of the structure was designed using 3D graphic statics, a novel method developed by the Block Research Group at ETH Zürich that extends the traditional 2D structural design technique to fully spatial systems [22]. Using polyhedral form and force diagrams, the method allows exploration and discovery of efficient and expressive spatial structures that are in compression-only, going beyond the arch or vault [23][24][25].…”

Section: Structural Geometry For Low-strength Materialsmentioning

confidence: 99%

Untitled

2017

IJSED

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MycoTree is a spatial branching structure made out of load-bearing mycelium components. Its geometry was designed using 3D graphic statics, utilising compression-only form to enable the weak material to perform structurally. Using only mycelium and bamboo, the structure represents a provocative vision of how one may move beyond the mining of our construction materials from the earth's crust to their cultivation; how achieving stability through geometry rather than through material strength opens up possibilities to use weaker materials structurally and safely; and ultimately, how newly developed cultivated materials in combination with informed structural design have the potential to propose an alternative to established building materials for a more sustainable construction industry.

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On the equilibrium of funicular polyhedral frames and convex polyhedral force diagrams

Cited by 75 publications

References 10 publications

Vector-based 3D graphic statics: A framework for the design of spatial structures based on the relation between form and forces

Vector-based 3D graphic statics: A framework for the design of spatial structures based on the relation between form and forces

Algebraic 3D graphic statics: Reciprocal constructions

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