纤维弹性细杆模型几何大变形静力学分析的有限元方法

Finite-Element Method of Statics Analysis of the Geometric Large Deformation of Fiber Elastic Thin Rod Model

以纺织工程中的气流辅助加捻纺纱为背景,以弹性细杆为纤维模型,对其几何位移大变形的非线性问题进行分析和讨论.采用空间杆单元有限元分析方法,导出了考虑轴力对弯曲影响的空间杆单元刚度矩阵,空间方位用欧拉角表示,几何非线性采用分步加载逐次逼近方法处理,建立了弹性细杆静力平衡方程组.对纤维弹性细杆有限元总体分析,运用Matlab模拟气流辅助加捻纺纱过程中纤维包缠的平衡状态.

Based on the airflow assisted twisting of yarn spinning in the textile engineering, using the elastic thin rod as the fiber model, the geometric nonlinear problems for this model＇s large deformation were analyzed and discussed. Using finite-element method and taking the bending problem influenced by the axial force into consideration, the spatial bar element stiffness matrixes were derived. The elastic thin rod static equilibrium equations were established using consecutive loading approach to deal with geometric nonlinearity problem and using Euler＇s angle to denote spatial orientation. The unity of the fiber elastic thin rod was analyzed by the finite-element method, and the static equilibrium configurations of the fiber in the airflow assisted twisting yarn for textile engineering were simulated by Matlab.