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Full-Text Articles in Physical Sciences and Mathematics
Liftings And Stresses For Planar Periodic Frameworks, Ciprian Borcea, Ileana Streinu
Liftings And Stresses For Planar Periodic Frameworks, Ciprian Borcea, Ileana Streinu
Computer Science: Faculty Publications
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.