Finite motions from periodic frameworks with added symmetry

Ross, Elissa and Schulze, Bernd and Whiteley, Walter (2011) Finite motions from periodic frameworks with added symmetry. International Journal of Solids and Structures, 48 (11-12). pp. 1711-1729. ISSN 0020-7683

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Abstract

Recent work from authors across disciplines has made substantial contributions to counting rules (Maxwell type theorems) which predict when an infinite periodic structure would be rigid or flexible while preserving the periodic pattern, as an engineering type framework, or equivalently, as an idealized molecular framework. Other work has shown that for finite frameworks, introducing symmetry modifies the previous general counts, and under some circumstances this symmetrized Maxwell type count can predict added finite flexibility in the structure. In this paper we combine these approaches to present new Maxwell type counts for the columns and rows of a modified orbit matrix for structures that have both a periodic structure and additional symmetry within the periodic cells. In a number of cases, this count for the combined group of symmetry operations demonstrates there is added finite flexibility in what would have been rigid when realized without the symmetry. Given that many crystal structures have these added symmetries, and that their flexibility may be key to their physical and chemical properties, we present a summary of the results as a way to generate further developments of both a practical and theoretic interest.

Item Type:
Journal Article
Journal or Publication Title:
International Journal of Solids and Structures
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2200/2211
Subjects:
?? framework rigidityperiodic symmetry crystal systems orbitsmechanics of materialsmodelling and simulationgeneral materials sciencemechanical engineeringapplied mathematicscondensed matter physicsmaterials science(all) ??
ID Code:
63629
Deposited By:
Deposited On:
24 Apr 2013 10:53
Refereed?:
Yes
Published?:
Published
Last Modified:
16 Jul 2024 09:20