Liftings and Stresses for Planar Periodic Frameworks

Authors

Ciprian Borcea, Rider University
Ileana Streinu, Smith CollegeFollow

Document Type

Article

Publication Date

6-2015

Abstract

We formulate and prove a periodic analog of Maxwell’s theorem relating stressed planar frameworks and their liftings to polyhedral surfaces with spherical topology. We use our lifting theorem to prove rigidity-theoretic properties for planar periodic pseudo-triangulations, generalizing their finite counterparts. These properties are then applied to questions originating in mathematical crystallography and materials science, concerning planar periodic auxetic structures and ultrarigid periodic frameworks.

Keywords

Maxwell’s theorem, periodic framework, periodic stress, liftings, periodic pseudo-triangulation, expansive motion, auxetics, ultrarigidity

Volume

53

Issue

4

First Page

747

Last Page

782

DOI

10.1007/s00454-015-9689-7

ISSN

1432-0444

Comments

Author’s submitted manuscript. A second version of the paper, as presented at the Symposium on Computational Geometry (SoCG'14), Kyoto, Japan, 2014, is also included.

Recommended Citation

Borcea, Ciprian and Streinu, Ileana, "Liftings and Stresses for Planar Periodic Frameworks" (2015). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/2