Equilibrium stressability of multidimensional frameworks

Oleg Karpenkov; Christian Müller; Gaiane Panina; Brigitte Servatius; Herman Servatius; Dirk Siersma

doi:10.1007/s40879-021-00523-3

Equilibrium stressability of multidimensional frameworks

Oleg Karpenkov, Christian Müller^*, Gaiane Panina, Brigitte Servatius, Herman Servatius, Dirk Siersma

^*Corresponding author for this work

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

Abstract

We prove an equilibrium stressability criterion for trivalent multidimensional frameworks. The criterion appears in different languages: (1) in terms of stress monodromies, (2) in terms of surgeries, (3) in terms of exact discrete 1-forms, and (4) in Cayley algebra terms.

Original language	English
Pages (from-to)	33-61
Number of pages	29
Journal	European Journal of Mathematics
Volume	8
Issue number	1
DOIs	https://doi.org/10.1007/s40879-021-00523-3
Publication status	Published - Mar 2022

Bibliographical note

Funding Information:
The collaborative research on this article was initiated during “Research-In-Groups” programs of ICMS Edinburgh, UK. The authors are grateful to ICMS for hospitality and excellent working conditions. Christian Müller gratefully acknowledges the support of the Austrian Science Fund (FWF) through projects P 29981. The authors acknowledge TU Wien Bibliothek for financial support through its Open Access Funding Programme.

Publisher Copyright:
© 2022, The Author(s).

Funding

The collaborative research on this article was initiated during “Research-In-Groups” programs of ICMS Edinburgh, UK. The authors are grateful to ICMS for hospitality and excellent working conditions. Christian Müller gratefully acknowledges the support of the Austrian Science Fund (FWF) through projects P 29981. The authors acknowledge TU Wien Bibliothek for financial support through its Open Access Funding Programme.

Keywords

Cayley algebra
Discrete multiplicative 1-form
Equilibrium stress
Framework
Lifting
Maxwell–Cremona correspondence
Self-stress
Tensegrity

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Cite this

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title = "Equilibrium stressability of multidimensional frameworks",

abstract = "We prove an equilibrium stressability criterion for trivalent multidimensional frameworks. The criterion appears in different languages: (1) in terms of stress monodromies, (2) in terms of surgeries, (3) in terms of exact discrete 1-forms, and (4) in Cayley algebra terms.",

keywords = "Cayley algebra, Discrete multiplicative 1-form, Equilibrium stress, Framework, Lifting, Maxwell–Cremona correspondence, Self-stress, Tensegrity",

author = "Oleg Karpenkov and Christian M{\"u}ller and Gaiane Panina and Brigitte Servatius and Herman Servatius and Dirk Siersma",

note = "Funding Information: The collaborative research on this article was initiated during “Research-In-Groups” programs of ICMS Edinburgh, UK. The authors are grateful to ICMS for hospitality and excellent working conditions. Christian M{\"u}ller gratefully acknowledges the support of the Austrian Science Fund (FWF) through projects P 29981. The authors acknowledge TU Wien Bibliothek for financial support through its Open Access Funding Programme. Publisher Copyright: {\textcopyright} 2022, The Author(s).",

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doi = "10.1007/s40879-021-00523-3",

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AU - Müller, Christian

AU - Panina, Gaiane

AU - Servatius, Brigitte

AU - Servatius, Herman

AU - Siersma, Dirk

N1 - Funding Information: The collaborative research on this article was initiated during “Research-In-Groups” programs of ICMS Edinburgh, UK. The authors are grateful to ICMS for hospitality and excellent working conditions. Christian Müller gratefully acknowledges the support of the Austrian Science Fund (FWF) through projects P 29981. The authors acknowledge TU Wien Bibliothek for financial support through its Open Access Funding Programme. Publisher Copyright: © 2022, The Author(s).

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KW - Discrete multiplicative 1-form

KW - Equilibrium stress

KW - Framework

KW - Lifting

KW - Maxwell–Cremona correspondence

KW - Self-stress

KW - Tensegrity

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Equilibrium stressability of multidimensional frameworks

Abstract

Bibliographical note

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Keywords

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