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arXiv · 1501.03549

Liftings and stresses for planar periodic frameworks

Ciprian S. Borcea·Ileana Streinu
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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.

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Ciprian S. Borcea, Ileana Streinu. 2015-01-15. Liftings and stresses for planar periodic frameworks. https://arxiv.org/abs/1501.03549

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