基于离散微分几何(DDG)方法模拟柔性结构非线性行为的教程

柔性弹性结构，如梁、棍、纸带、板和壳， exhibit complex nonlinear dynamical behaviors，这些行为是广泛应用于工程和科学领域的核心问题，包括软体机器人、可部署结构和生物医学器件。虽然已developed various numerical methods to simulate these behaviors，但 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. 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, simulation frameworks, and MATLAB implementation, with examples spanning dynamic systems, geometric and material nonlinearities, and external interactions like magnetics and fluids, culminating in practical insights and future directions. By offering a comprehensive and practical guide, together with open-source MATLAB code, this tutorial aims to facilitate the broader adoption of DDG-based numerical tools among researchers and engineers in computational mechanics, applied mathematics, and structural design.