Frameworks with crystallographic symmetry
Frameworks with crystallographic symmetry
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DOI：
10.1098/rsta.2012.0143
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发表时间：
2014-02-13
期刊：
影响因子：
5
通讯作者：
Streinu, Ileana
中科院分区：
文献类型：
--
作者：
Borcea, Ciprian S.;Streinu, Ileana
从任意维欧几里得空间中周期性条节结构的一般变形理论的角度研究了具有晶体学对称性的周期框架。结果表明，自然参数化为具有指定图形和对称性的框架族提供了仿射截面描述。获得了位移相变的简单几何设置。导出最小刚性周期图的实现数量的上限。
Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in Euclidean spaces of arbitrary dimension. It is shown that natural parametrizations provide affine section descriptions for families of frameworks with a specified graph and symmetry. A simple geometrical setting for displacive phase transitions is obtained. Upper bounds are derived for the number of realizations of minimally rigid periodic graphs.