用区间牛顿法跟踪结构的后屈曲路径

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.

Tracing Post-buckling Path of Structures by Interval Newton Method

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.