Frameworks with crystallographic symmetry
Ciprian S. Borcea, Ileana Streinu
TL;DR
This paper explores the deformation theory of periodic frameworks with crystallographic symmetry, providing new parametrizations, geometric insights into phase transitions, and bounds on realizations of minimally rigid structures.
Contribution
It introduces affine section descriptions for frameworks with given symmetry and graph, and derives bounds on the number of realizations of minimally rigid periodic graphs.
Findings
Affine section descriptions for symmetric frameworks
Geometric setting for diaplacive phase transitions
Upper bounds on realizations of minimally rigid periodic graphs
Abstract
Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in . It is shown that natural parametrizations provide affine section descriptions for families of frameworks with a specified graph and symmetry. A simple geometric setting for diaplacive phase transitions is obtained. Upper bounds are derived for the number of realizations of minimally rigid periodic graphs.
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Taxonomy
TopicsStructural Analysis and Optimization · Advanced Materials and Mechanics · Quasicrystal Structures and Properties