Bi-directional algebraic graphic statics

Vedad Alic; Daniel Åkesson

doi:10.1016/j.cad.2017.08.003

Bi-directional algebraic graphic statics

Vedad Alic, Daniel Åkesson

Research output: Contribution to journal › Article › peer-review

Abstract

A pre-existing algebraic graphic statics method is extended to allow for interactive manipulations of the force diagram, from which an updated form diagram is determined. Newton's method is used to solve a set of non-linear equations, and the required Jacobian matrix is derived. Additional geometric constraints on the form diagram are introduced, and methods for improving the robustness of the method are presented. We discuss the implementation of the method as a back-end to an interactive application, and demonstrate the usability of the method in several examples where the qualities of directly manipulating the force diagram are emphasized.

Original language	English
Pages (from-to)	26-37
Number of pages	12
Journal	Computer-Aided Design
Volume	93
DOIs	https://doi.org/10.1016/j.cad.2017.08.003
Publication status	Published - 2017 Dec 1

Subject classification (UKÄ)

Algebra and Logic

Free keywords

Conceptual design
Force diagram manipulations
Graph theory
Interactive graphic statics
Matrix analysis of structures
Reciprocal figures

Access to Document

10.1016/j.cad.2017.08.003

1 Doctoral Thesis (compilation)

Computational Methods in Conceptual Structural Design
Alic, V., 2018, Lund University. Faculty of Engineering (LTH), Division of Structural Mechanics. 175 p.
Research output: Thesis › Doctoral Thesis (compilation)

Open Access
File

Cite this

@article{f236a3090bc74c0ea68e84c664969f67,

title = "Bi-directional algebraic graphic statics",

abstract = "A pre-existing algebraic graphic statics method is extended to allow for interactive manipulations of the force diagram, from which an updated form diagram is determined. Newton's method is used to solve a set of non-linear equations, and the required Jacobian matrix is derived. Additional geometric constraints on the form diagram are introduced, and methods for improving the robustness of the method are presented. We discuss the implementation of the method as a back-end to an interactive application, and demonstrate the usability of the method in several examples where the qualities of directly manipulating the force diagram are emphasized.",

keywords = "Conceptual design, Force diagram manipulations, Graph theory, Interactive graphic statics, Matrix analysis of structures, Reciprocal figures",

author = "Vedad Alic and Daniel {\AA}kesson",

year = "2017",

month = dec,

day = "1",

doi = "10.1016/j.cad.2017.08.003",

language = "English",

volume = "93",

pages = "26--37",

journal = "Computer-Aided Design",

issn = "0010-4485",

publisher = "Elsevier",

}

TY - JOUR

T1 - Bi-directional algebraic graphic statics

AU - Alic, Vedad

AU - Åkesson, Daniel

PY - 2017/12/1

Y1 - 2017/12/1

N2 - A pre-existing algebraic graphic statics method is extended to allow for interactive manipulations of the force diagram, from which an updated form diagram is determined. Newton's method is used to solve a set of non-linear equations, and the required Jacobian matrix is derived. Additional geometric constraints on the form diagram are introduced, and methods for improving the robustness of the method are presented. We discuss the implementation of the method as a back-end to an interactive application, and demonstrate the usability of the method in several examples where the qualities of directly manipulating the force diagram are emphasized.

AB - A pre-existing algebraic graphic statics method is extended to allow for interactive manipulations of the force diagram, from which an updated form diagram is determined. Newton's method is used to solve a set of non-linear equations, and the required Jacobian matrix is derived. Additional geometric constraints on the form diagram are introduced, and methods for improving the robustness of the method are presented. We discuss the implementation of the method as a back-end to an interactive application, and demonstrate the usability of the method in several examples where the qualities of directly manipulating the force diagram are emphasized.

KW - Conceptual design

KW - Force diagram manipulations

KW - Graph theory

KW - Interactive graphic statics

KW - Matrix analysis of structures

KW - Reciprocal figures

U2 - 10.1016/j.cad.2017.08.003

DO - 10.1016/j.cad.2017.08.003

M3 - Article

AN - SCOPUS:85028995647

SN - 0010-4485

VL - 93

SP - 26

EP - 37

JO - Computer-Aided Design

JF - Computer-Aided Design

ER -

Bi-directional algebraic graphic statics

Abstract

Subject classification (UKÄ)

Free keywords

Access to Document

Fingerprint

Research output

Computational Methods in Conceptual Structural Design

Cite this