标题： 通用随机张力整体结构的刚性 显示英文标题

标题： Rigidity of generic random tensegrity structures

摘要： 许多机械结构，无论是工程结构还是生物结构，都结合了厚重的刚性元件，如骨骼和梁，以及轻质的柔性元件，如缆绳和膜。这些结构被称为张力脊结构，反映了缆绳只能承受拉伸张力。我们通过耗尽三角形晶格的模拟来建模这类系统，在受拉伸边界条件约束的情况下最小化张力脊结构的能量。当缆绳和支撑杆（仅能承受压缩张力）数量相等时，一个缆绳和一个支撑杆共同对刚度的贡献与一个杆相当，在剪切应变的情况下，两者的贡献相等。由于在刚度转变处存在高度非仿射变形，即使在全局压缩（膨胀）下，缆绳（支撑杆）的贡献也可能显著，尽管缆绳无法抵抗局部压缩。此外，我们发现当相邻元件倾向于彼此远离时，如在真实系统中常见的情况，缆绳与其他缆绳之间的相互作用比缆绳与支撑杆之间的相互作用在支撑应力方面要强得多。这些现象为处于机械稳定性阈值的各种现实的、无序系统提供了新的见解。 显示英文摘要

摘要： Many mechanical structures, both engineered and biological, combine heavy rigid elements such as bones and beams with lightweight flexible ones such as cables and membranes. These are referred to as tensegrities, reflecting that cables can only support extensile tension. We model such systems via simulations of depleted triangular lattices in which we minimize the energies of tensegrities subject to strained boundary conditions. When there are equal numbers of cables and struts (which support only compressive tension), a cable and a strut together each contribute as much toward rigidity as a rod, with the two contributions being equal in the case of shear strain. Due to the highly nonaffine deformations at the rigidity transitions, the contribution of a cable (strut) can be significant even under global compression (dilation) despite a cable's inability to resist local compression. Further, we find that when neighboring elements tend to point away from one another, as is common in real systems, cables interact significantly more strongly with other cables than do cables with struts in supporting stress. These phenomena shed new light on a variety of realistic, disordered systems at the threshold of mechanical stability.