逆向离散弹性杆
Inverse Discrete Elastic Rod
AI总结：
本文提出逆向离散弹性杆方法，通过将逆问题转化为静态平衡，实现高效且准确的逆向设计，适用于多种实际应用。
摘要：
逆向设计细长弹性结构在计算机图形学、柔性电子、生物医学设备和软机器人等领域具有广泛的应用。然而，传统基于优化的方法通常比正向动态模拟慢多个数量级，并且通常施加限制性的边界条件。在本文中，我们提出了一种逆向离散弹性杆（inverse-DER）方法，该方法能够在一般加载和边界条件下实现高效且准确的逆向设计。通过将逆问题重新表述为参考配置中的静态平衡，我们的方法在计算效率上与正向模拟相当，同时保持了高保真度。该框架允许快速确定未变形的几何形状，这些形状在受激励或加载时会自然变形为所需的靶向形状。我们通过物理原型和正向模拟验证了该方法，证明了其准确性、鲁棒性和在实际设计应用中的潜力。
英文摘要：
Inverse design of slender elastic structures underlies a wide range of applications in computer graphics, flexible electronics, biomedical devices, and soft robotics. Traditional optimization-based approaches, however, are often orders of magnitude slower than forward dynamic simulations and typically impose restrictive boundary conditions. In this work, we present an inverse discrete elastic rods (inverse-DER) method that enables efficient and accurate inverse design under general loading and boundary conditions. By reformulating the inverse problem as a static equilibrium in the reference configuration, our method attains computational efficiency comparable to forward simulations while preserving high fidelity. This framework allows rapid determination of undeformed geometries for elastic fabrication structures that naturally deform into desired target shapes upon actuation or loading. We validate the approach through both physical prototypes and forward simulations, demonstrating its accuracy, robustness, and potential for real-world design applications.
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