Algebraic 3D graphic statics: Reciprocal constructions

Research output: Contribution to journalJournal articleResearchpeer-review

Márton Hablicsek, Masoud Akbarzadeh, Yi Guo

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 diagrams 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.

Original languageEnglish
JournalCAD Computer Aided Design
Volume108
Pages (from-to)30-41
Number of pages12
ISSN0010-4485
DOIs
Publication statusPublished - 2019

    Research areas

  • Algebraic three-dimensional graphic statics, Constraint manipulation of polyhedral diagrams, Geometric degrees of freedom, Polyhedral reciprocal diagrams, Static degrees of indeterminacies, Tension and compression combined polyhedra

ID: 215778449