弧长控制类方法使用中若干问题的探讨与改进

在结构非线性跟踪分析中，弧长控制类方法和能量控制类方法是两类最主要的方法。近年来，各类弧长方法由于概念简单明了、计算方便可靠而广为采用。本文首先对几种主要弧长方法的使用进行回顾和比较，并就跟踪失败的可能情况作简单探讨，进而针对部分可能失败的情况提出改进措施。再以一个同时存在跳跃及跳回现象且具有分枝路径的问题为例，将这几种弧长方法用于其变形全过程的跟踪分析，来验证所提出的改进措施，比较这几种弧长方法的跟踪能力。最后给出使用这些弧长方法的几点结论。

Discussion on some problems in using arc length type methods and their improvement

The arc length type methods and energy type methods are two main types of control methods used in structural nonlinear tracing analysis, but the former has been widely used due to the explicitness and clarity in conception, as well as the convenience and reliability in calculation. In this paper, several main arc length type methods are reviewed and compared, and the main possible reasons of failures in tracing analysis are briefly discussed. Then some suggestions of improvement are presented, and an example having snapping through, snapping back phenomena and bifurcation paths is used to compare the tracing ability of the conventional arc length type methods with the improved arc length methods. Finally, some conclusions are drawn in using the arc length type methods.