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Symmetry-extended counting rules for periodic frameworks.

Guest, SD and Fowler, PW (2014) Symmetry-extended counting rules for periodic frameworks. Philos Trans A Math Phys Eng Sci, 372. 20120029-. ISSN 1364-503X

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Abstract

A symmetry-adapted version of the Maxwell rule appropriate to periodic bar-and-joint frameworks is obtained, and is further extended to body-and-joint systems. The treatment deals with bodies and forces that are replicated in every unit cell, and uses the point group isomorphic to the factor group of the space group of the framework. Explicit expressions are found for the numbers and symmetries of detectable mechanisms and states of self-stress in terms of the numbers and symmetries of framework components. This approach allows detection and characterization of mechanisms and states of self-stress in microscopic and macroscopic materials and meta-materials. Illustrative examples are described. The notion of local isostaticity of periodic frameworks is extended to include point-group symmetry.

Item Type: Article
Uncontrolled Keywords: frameworks periodicity symmetry
Subjects: UNSPECIFIED
Divisions: Div D > Structures
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 11:25
Last Modified: 21 Apr 2014 01:09
DOI: 10.1098/rsta.2012.0029

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