States of self-stress in symmetric frameworks and applications

Schulze, Bernd and Miller, Cameron and Mazurek, Arek and Baker, William (2022) States of self-stress in symmetric frameworks and applications. International Journal of Solids and Structures, 234-23: 111238. ISSN 0020-7683

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We use the symmetry-extended Maxwell rule established by Fowler and Guest to detect states of self-stress in symmetric planar frameworks. The dimension of the space of self-stresses that are detectable in this way may be expressed in terms of the number of joints and bars that are unshifted by various symmetry operations of the framework. Therefore, this method provides an efficient tool to construct symmetric frameworks with many ‘fully-symmetric’ states of self-stress, or with ‘anti-symmetric’ states of self-stress. Maximising the number of independent self-stresses of a planar framework, as well as understanding their symmetry properties, has important practical applications, for example in the design and construction of gridshells. We show the usefulness of our method by applying it to some practical examples.

Item Type:
Journal Article
Journal or Publication Title:
International Journal of Solids and Structures
Additional Information:
This is the author’s version of a work that was accepted for publication in International Journal of Solids and Structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Solids and Structures, 234-235, 2022 DOI: 10.1016/j.ijsolstr.2021.111238
Uncontrolled Keywords:
?? symmetryrigiditybar-joint frameworkequilibrium stressgridshell structuremechanics of materialsmodelling and simulationgeneral materials sciencemechanical engineeringapplied mathematicscondensed matter physicsmaterials science(all) ??
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Deposited On:
10 Sep 2021 08:15
Last Modified:
16 Jul 2024 11:42