基于杆与铰链方法的快速剪纸模拟
Rapid Kirigami Simulation using the Bar & Hinge Approach
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中文总结 AI 辅助
本文提出一种基于杆与铰链方法的广义降阶剪纸模拟模型，计算效率较有限元方法提升至少10倍，变形预测误差小于5%，可用于复杂剪纸结构的模拟与高通量设计探索。
中文摘要 AI 辅助
剪纸（Kirigami）是一种通过切割薄片实现的艺术，具备形状变形、可拉伸性和适应性等独特特性，可应用于可部署和可重构结构。虽然有限元（FE）方法被广泛用于分析剪纸结构，但其计算密集且易出现收敛问题。另一方面，现有的用于评估剪纸的简化和理论模型通常局限于特定设计和分析场景。本文提出一种基于杆与铰链方法的广义、计算高效的降阶模型，用于分析任意剪纸系统。该模型用桁架杆、弯曲铰链和扭转弹簧表示整个剪纸结构，捕捉系统的变形和内力。我们推导了经历拉伸和面外弯曲变形的剪纸结构，以及仅经历面内拉伸和旋转的结构的刚度表达式。通过与有限元分析以及单切口剪纸设计和具有多个切口的更复杂设计的实验数据进行比较，验证了该模型的准确性和鲁棒性。我们的结果显示，变形预测的差异小于5%，且与有限元模拟相比，计算速度至少提升了一个数量级。此外，我们通过模拟复杂场景展示了该模型的能力，包括覆有剪纸的爬行器、高通量属性空间探索以及受面内剪纸启发的超材料。这些示例展示了超越传统有限元方法实际限制的计算能力，可实现大变形结构模拟和高通量设计探索。
英文摘要
Kirigami, the art of cutting sheets, offers unique characteristics such as shape morphing, stretchability, and adaptability, with applications in deployable and reconfigurable structures. While Finite Element (FE) approaches are widely used to analyze kirigami structures, they are computationally intensive and prone to convergence issues. On the other hand, existing simplified and theoretical models for evaluating kirigami are typically restricted to specific designs and analytical scenarios. This paper proposes a generalized, computationally efficient reduced-order model based on the bar and hinge approach for analyzing any kirigami system. The model represents the entire kirigami structure using truss bars, bending hinges, and torsional springs, capturing both the deformation and internal forces of the system. We derive stiffness expressions for kirigami structures that experience stretching and out-of-plane bending deformations, as well as for structures that experience only in-plane stretching and rotations. The accuracy and robustness of the model are validated through comparisons with FE analysis and experimental data on both single-cut kirigami designs and more complex designs with multiple cuts. Our results demonstrate less than 5% difference in deformation predictions and achieve at least a tenfold computational speedup compared to FE simulations. Additionally, we demonstrate the model's capabilities through simulating complex scenarios, including kirigami-skinned crawlers, high-throughput property-space exploration, and in-plane kirigami-inspired metamaterials. These examples demonstrate computational capabilities that enable large-deformation structural simulations and high-throughput design exploration beyond the practical limits of conventional FE methods.
