Year: 2015
Type: preprint
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 deformation and rigidity-theoretic properties for planar periodic pseudo-triangulations, generalizing features known for 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.
Source: arXiv (Cornell University)
Authors: Borcea, Ciprian S., Streinu, Ileana
Institutions: Rider University, Smith College
Language: English
Subfield: Civil and Structural Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2953276157