A Tutorial on Simulating Nonlinear Behaviors of Flexible Structures With the Discrete Differential Geometry Method

作者：Weicheng Huang, Zhuonan Hao, Jiahao Li, Dezhong Tong, Kexin Guo, Yingchao Zhang, Huajian Gao, K. Jimmy Hsia, Mingchao Liu · 发表于：Applied Mechanics Reviews · 年份：2025 · DOI：10.1115/1.4069025 · 被引用次数：30 · 研究领域：Vibration and Dynamic Analysis、Dynamics and Control of Mechanical Systems、Innovations in Concrete and Construction Materials

Abstract Flexible elastic structures, such as beams, rods, ribbons, plates, and shells, exhibit complex nonlinear dynamical behaviors that are central to a wide range of engineering and scientific applications, including soft robotics, deployable structures, and biomedical devices. While various numerical methods have been developed to simulate these behaviors, many conventional approaches struggle to simultaneously capture geometric and material nonlinearities, as well as nonlinear external interactions, particularly in highly deformable and dynamically evolving systems. The discrete differential geometry (DDG) method has emerged as a robust and efficient numerical framework that intrinsically preserves geometric properties, accommodates material nonlinearity, and accurately models interactions with external environments and fields. By directly discretizing geometric and mechanical quantities, DDG provides an accurate, stable, and efficient approach to modeling flexible structures, addressing key limitations of traditional numerical methods. This tutorial provides a systematic introduction to the DDG method for simulating nonlinear behaviors in flexible structures. It covers DDG theory, numerical framework, and simulation implementation, with examples spanning dynamic systems, geometric and material nonlinearities, and external interactions like magnetics, fluids, and contact, culminating in practical insights and future directions. By offering a comprehensive and practical ...