摘要
有限转动角的计算和迭加方法与线位移不同。为了能利用修正的 Lagrangian法及带有动坐标的迭代法来分析三维空间大转动梁的受力和变形 ,研究了三维空间大转动梁的共轴转动机理 ,引入了伪矢量的概念 ,严格地应用数学和弹性力学理论导出了相关的公式 ,给出了迭代过程。解决了分析空间大转动梁的带有动坐标的迭代法所涉及到的有关有限转动的两个关键问题 :(1 )单元畸变中节点转角位移的计算 ;(2 )迭代过程中新的一轮转角位移的确定。文中所给出的公式和迭代过程在计算机上易于操作 ,数值结果也证明了公式的正确性。
The method for computing finite rotations is different from that of the translation displacements. To analyze the stress and deformation of 3-D spatial beams by large rotations in 3-D space by using the updated Lagrangian descriptions and moving coordinate iterative method, a new co-rotational procedure is studied. Iteration procedures are developed by introducing of the pseudo-vector concept and using the mathematics and elasticity theories. Two critical problems in usage of the moving coordinate iterative method to analyze 3-D spatial beams undergone by large rotations are encountered, i.e. how to compute the nodal rotational displacements for an deformed beam and how to update the rotations during the iteration process. The formulae are easy to be coded. Numerical data demonstrate the correctness of the developed formulae.
出处
《南京航空航天大学学报》
EI
CAS
CSCD
北大核心
2004年第6期718-722,共5页
Journal of Nanjing University of Aeronautics & Astronautics
基金
Smith International Inc.基金 (2 0 0 1 -0 1 3 -1 3 L)资助项目
关键词
有限元法
迭代法
有限转动
共轴转动
伪矢量
钻柱
finite element method
iterative method
finite rotations
co-rotation
pseudo-vector
drillstrings
