基于等几何分析方法的柔性布料动力学研究

Cloth simulation has obtained widespread attention and application in the clothing design, virtual reality, film industry, e-commerce and other industries. However, cloth models based on mechanics has been gradually applied until recently. The main reason is that fabric products usually have complex topological structure, special materials, and are prone to hanging, bending, folding, winkling, and have contact/collision with the environment, and real-time simulation is usually needed. Therefore, the study of cloth dynamic simulation has important scientific significance and application prospects. This project studies cloth simulation based on isogeometric analysis. The method can use the same geometric and analytical model, and construct accurate, complex, high-order continuous finite element model and its refinement algorithm, which is suitable for cloth simulation needs. The main research contents of the project include: (1) accurate kinematic model based on NURBS and T-splines; (2) dynamic model based on continuum mechanics and nonlinear finite element theory; (3) stable and fast explicit/implicit mixed numerical integration algorithm; (4) accurate and efficient contact/collision detection and response algorithm; (5) model test. Through the research of this project, the isogeometric analysis theory and algorithm of flexible cloth dynamics can be formed to explore the influence mechanism of fabric material and woven structure on the cloth's dynamic shape, and improve the precision and efficiency of the simulation.

布料仿真在服装设计、虚拟现实、电影工业、电子商务等行业得到了广泛的关注和应用，但基于力学模型的仿真技术直到近年来才逐渐得到应用。主要原因是布料产品通常结构复杂，材质特殊，易发生悬垂、弯曲、褶皱、摺叠、接触/碰撞等复杂力学现象，仿真实时性要求高。因此，研究布料动力学仿真具有重要的科学意义和应用前景。本项目研究基于等几何分析的布料动力学仿真方法。该方法可将几何与分析模型统一，构造精确、复杂、高阶连续的有限元模型及细化算法，适于布料仿真需求。项目主要研究内容包括：(1)基于NURBS和T样条的精确运动学模型；(2)基于连续介质力学和非线性有限元理论的动力学模型；(3)稳定、快速的显式/隐式混合数值积分算法；(4)准确、高效的接触/碰撞检测、响应算法；(5)模型试验。通过本项目的研究，形成柔性布料动力学的等几何分析理论及算法，探索布料材质、机织结构对布料形态的影响机理，提高仿真的精度和效率。

项目研究了柔性布料动力学的等几何分析理论，主要研究内容包括：基于等几何分析理论的柔性布料几何/分析统一的运动学模型，基于连续介质力学理论的柔性布料动力学模型以及面向稳定、快速性要求的数值积分方法和接触/碰撞检测算法，并通过实验进行了对比验证。项目取得的主要研究进展包括：在等几何分析框架内，研究了基于单元的mortar积分算法，可在满足精度要求的同时，有效降低不匹配网格耦合对板壳界面网格细分的需求，提高复杂拓扑结构建模的可行性和效率；在等几何分析框架内，研究了基于截断层次样条的多层次网格细分算法，结合AABB层次树算法，可有效提升柔性布料接触/碰撞检测的效率以及接触区域网格质量；针对柔性布料小膜应变的特点，研究了KL板壳理论的简化修正形式，在实现了模型的高阶连续性，无转动自由度以及缩减了系统方程规模的同时，在满足精度要求的前提下，有效提高了动力学方程中各离散项的数值积分效率。项目研究成果对于柔性布料及其他板壳结构的动力学研究具有相应的学术价值，后续经转化后，可用于虚拟现实等现实应用。