平面周期性框架的提升与应力
Liftings and stresses for planar periodic frameworks.
作者信息
Borcea Ciprian, Streinu Ileana
机构信息
Department of Mathematics, Rider University, Lawrenceville, NJ 08648, USA.
Department of Computer Science, Smith College, Northampton, MA 01063, USA.
出版信息
Discrete Comput Geom. 2015 Jun 1;53(4):747-782. doi: 10.1007/s00454-015-9689-7. Epub 2015 Apr 18.
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.
我们阐述并证明了麦克斯韦定理的一个周期性类似物，该定理将受力平面框架及其提升与具有球面拓扑的多面体表面联系起来。我们利用提升定理证明了平面周期性伪三角剖分的变形和刚性理论性质，推广了其有限对应物已知的特征。然后将这些性质应用于源自数学晶体学和材料科学的问题，涉及平面周期性负泊松比结构和超刚性周期性框架。
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