Generic combinatorial rigidity of periodic frameworks

By Justin Malestein, Louis Theran. 2010

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Abstract We give a combinatorial characterization of generic minimal rigidity for planar periodic frameworks . The characterization is a true analogue of the Maxwell–Laman Theorem from rigidity theory: it is stated in terms of a finite combinatorial object and the conditions are checkable by polynomial time combinatorial algorithms. To prove our rigidity theorem we introduce and develop periodic direction networks and Z 2 - graded-sparse colored graphs .

Subfields: Biomedical Engineering, Civil and Structural Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/51584696d5e2700567ae5aaa519ca5a4d22b075b