AI 中文总结
本文提出适用于任意形状平面梁大位移大转动分析的共旋格式，采用NURBS基函数，经多类数值算例验证其收敛性好、大变形预测准确且可缓解闭锁，对非均匀截面等梁性能稳健。
AI 中文摘要
本文提出一种平面共旋梁格式，用于分析具有任意初始几何形状的梁的大位移与大转动问题。将局部坐标系附着于每个梁微段并跟随其刚体平移与转动，可得到适用于高阶基函数的一致运动学描述。引入辅助直参考构型，使得任意初始构型与当前变形构型均可相对于同一参考进行描述，从而可在共旋框架内处理任意初始几何。该框架具有通用性，适用于多种高阶基函数，本研究采用非均匀有理B样条（NURBS）基函数以发挥其优异的几何表示能力与光滑性。通过五个数值算例评估所提格式的性能，涵盖静载、后屈曲、动态及静动耦合情形。结果表明，该格式具有优异的收敛性，可准确预测大变形响应，无需额外处理即可有效缓解闭锁现象，且对非均匀截面梁及空间变曲率梁表现出稳健性能。
英文摘要
A planar co-rotational beam formulation is proposed for the large displacement and large rotation analysis of beams with arbitrary initial geometries. A local frame is attached to each differential beam segment and follows its rigid body translation and rotation, enabling a consistent kinematic description suitable for higher-order basis functions. An auxiliary straight reference configuration is introduced so that both the arbitrary initial configuration and the current deformed configuration can be described relative to a common reference, enabling arbitrary initial geometries to be treated within the co-rotational framework. While the framework is general and applicable to a wide range of higher-order basis functions, Non-Uniform Rational B-Splines (NURBS) basis functions are adopted in this study to exploit their superior geometric representation and smoothness. The performance of the proposed formulation is evaluated through five numerical examples, including static, post-buckling, dynamic, and coupled static-dynamic cases. The results demonstrate excellent convergence, accurate prediction of large-deformation responses, effective mitigation of locking without additional treatment, and robust performance for beams with non-uniform cross-sections and spatially varying curvature.
