北京航空航天大学学报 ›› 2000, Vol. 26 ›› Issue (5): 535-538.

• 论文 • 上一篇    下一篇

用区间牛顿法跟踪结构的后屈曲路径

仝宗凯, 王寿梅, 邱志平   

  1. 北京航空航天大学 飞行器设计与应用力学系
  • 收稿日期:1999-04-05 出版日期:2000-05-31 发布日期:2010-09-27
  • 作者简介:仝宗凯(1971-),男,山西大同人,博士生,100083,北京.
  • 基金资助:

    国家自然科学基金资助项目(19602006)

Tracing Post-buckling Path of Structures by Interval Newton Method

TONG Zong-kai, WANG Shou-mei, QIU Zhi-ping   

  1. Beijing University of Aeronautics and Astronautics, Dept. of Flight Vehicle Design and Applied Mechanics
  • Received:1999-04-05 Online:2000-05-31 Published:2010-09-27

摘要: 结构后屈曲分析传统上都是采用弧长控制法来处理.考虑到区间牛顿法求解非线性方程组的全局收敛性质,本文建议将这种方法用于跟踪结构后屈曲平衡路径.文内建立了将区间牛顿法用于有限元控制方程的增量求解迭代格式.在低载荷水平下,为减少迭代次数采用了小区间半径.当时间步接近临界点时,方法可以自动搜索出屈曲前和屈曲后的2个平衡构形,然后在屈曲后构形基础上跟踪临界点后的路径,这样就可以避免在临界载荷处由于刚度矩阵奇异而使迭代不能继续的数值困难.典型的数值算例证实了新方法的有效性,同时也表明算法能毫不费力地处理所谓"位移回弹"(snap-back)问题.

Abstract: Post-buckling analysis was traditionally conducted by arc length method. In view of the feature of global convergence of the interval iteration method in solving nonlinear equation sets, an approach is proposed to apply this method in tracing post-buckling path of structures. An incremental solution scheme is introduced. Smaller interval radius is suggested to avoid excessive number of iterations at low loading levels. When time stepping approaches the critical point, two equilibrium configurations of pre and post-buckling can be detected automatically, which avoids iteration failure resulting from the singularity of stiffness matrix. The rest part of tracing is then conducted based on the later configuration. Validation of the new method is demonstrated by a typical numerical example. It also shows that the method can deal with the phenomenon so called Snap-back problems without additional efforts.

中图分类号: 


版权所有 © 《北京航空航天大学学报》编辑部
通讯地址:北京市海淀区学院路37号 北京航空航天大学学报编辑部 邮编:100191 E-mail:jbuaa@buaa.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发