Algebraic 3D graphic statics: Reciprocal constructions

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Standard

Algebraic 3D graphic statics : Reciprocal constructions. / Hablicsek, Márton; Akbarzadeh, Masoud; Guo, Yi.

I: CAD Computer Aided Design, Bind 108, 2019, s. 30-41.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Hablicsek, M, Akbarzadeh, M & Guo, Y 2019, 'Algebraic 3D graphic statics: Reciprocal constructions', CAD Computer Aided Design, bind 108, s. 30-41. https://doi.org/10.1016/j.cad.2018.08.003

APA

Hablicsek, M., Akbarzadeh, M., & Guo, Y. (2019). Algebraic 3D graphic statics: Reciprocal constructions. CAD Computer Aided Design, 108, 30-41. https://doi.org/10.1016/j.cad.2018.08.003

Vancouver

Hablicsek M, Akbarzadeh M, Guo Y. Algebraic 3D graphic statics: Reciprocal constructions. CAD Computer Aided Design. 2019;108:30-41. https://doi.org/10.1016/j.cad.2018.08.003

Author

Hablicsek, Márton ; Akbarzadeh, Masoud ; Guo, Yi. / Algebraic 3D graphic statics : Reciprocal constructions. I: CAD Computer Aided Design. 2019 ; Bind 108. s. 30-41.

Bibtex

@article{ec0d52b8d0d342529e260803ac366ec4,
title = "Algebraic 3D graphic statics: Reciprocal constructions",
abstract = "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.",
keywords = "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",
author = "M{\'a}rton Hablicsek and Masoud Akbarzadeh and Yi Guo",
year = "2019",
doi = "10.1016/j.cad.2018.08.003",
language = "English",
volume = "108",
pages = "30--41",
journal = "CAD Computer Aided Design",
issn = "0010-4485",
publisher = "Elsevier Limited",

}

RIS

TY - JOUR

T1 - Algebraic 3D graphic statics

T2 - Reciprocal constructions

AU - Hablicsek, Márton

AU - Akbarzadeh, Masoud

AU - Guo, Yi

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Algebraic three-dimensional graphic statics

KW - Constraint manipulation of polyhedral diagrams

KW - Geometric degrees of freedom

KW - Polyhedral reciprocal diagrams

KW - Static degrees of indeterminacies

KW - Tension and compression combined polyhedra

UR - http://www.scopus.com/inward/record.url?scp=85056894749&partnerID=8YFLogxK

U2 - 10.1016/j.cad.2018.08.003

DO - 10.1016/j.cad.2018.08.003

M3 - Journal article

AN - SCOPUS:85056894749

VL - 108

SP - 30

EP - 41

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

SN - 0010-4485

ER -

ID: 215778449