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Abstract：
In this paper, the nonlinear mechanical response of elastic cable structures under mechanical load is studied based on the discrete catenary theory. A cable net is discretized into multiple nodes and edges in our numerical approach, which is followed by an analytical formulation of the elastic energy and the associated Hessian matrix to realize the dynamic simulation. A fully implicit framework is proposed based on the discrete differential geometry (DDG) theory. The equilibrium configuration of a target object is derived by adding damping force into the system, known as the dynamic relaxation method. The mechanical response of a single suspended cable is investigated and compared with the analytical solution for cross-validation. A more intricate scenario is further discussed in detail, where a structure consisting of multiple slender cables is connected through joints. Utilizing the robustness and efficiency of our discrete numerical framework, a systematic parameter sweep is performed to quantify the force displacement relationships of nets with the different number of cables and different directions of fibers. Finally, an empirical scaling law is provided to account for the rigidity of elastic cable net in terms of its geometric properties, material characteristics, component numbers, and cable orientations. Our results would provide new insight in revealing the connections between flexible structures and tensegrity structures, and could motivate innovative designs in both mechanical and civil engineered equipment.
摘要：
在本文中,基于离散悬链线理论，研究了弹性索结构在机械载荷作用下的非线性力学响应。在我们的数值方法中，电缆网被离散为多个节点和边缘，然后是弹性能量和相关的Hessian矩阵的解析公式，以实现动态模拟。基于离散微分几何（DDG）理论，提出了一种全隐式框架。通过向系统中添加阻尼力来得出目标对象的平衡配置，称为动态松弛法。研究了单个悬挂电缆的机械响应，并将其与分析解决方案进行了比较，以进行交叉验证。进一步详细讨论了一个更复杂的场景，由多根细长电缆组成的结构通过接头连接。利用我们离散数值框架的鲁棒性和效率，进行了系统参数扫描，以量化网络与不同数量的电缆和不同方向的纤维的力位移关系。最后,根据弹性索网的几何特性，提供了经验比例定律来解释弹性索网的刚度，材料特性,组件编号,和电缆方向。我们的结果将为揭示柔性结构和张力结构之间的联系提供新的见解，并可以激发机械和土木工程设备的创新设计。
