Abstract: Arc length method can track nonlinear equilibrium configuration，but it is greatly affected by the initial setting load values. As a result，modified arc length method，aimed at solving the problem，works out expulsion process of diaphragms better. Several materials，such as 3012 titanium alloy，pure titanium and an ideal material，were chosen to study effects of residual stain on multi-expulsion behaviors for spherical-cone diaphragms based on modified arc length method by Finite Element Method(FEM). Positive expulsion and back reversal processes of 3012 titanium alloy diaphragms were not as good as that of pure titanium diaphragms. The former had severe eccentricity problems along with folding，and the eccentricity value reached at 60mm during back reversal process after 98 percent positive expulsion. Ideal material diaphragms all had severe eccentricity problems during back reversal process after positive expulsion of different percents，and the maximum eccentricity value was larger than 80mm. Pure titanium diaphragms had marked eccentricity phenomena only when back reversal process is at 98 percent positive expulsion，and the eccentricity value was about 10mm. Materials with no residual strain reduce structural stiffness of diaphragms，and coexist with the feature of initial elastic modulus being smaller. These factors are disadvantageous to multi-expulsion behaviors of diaphragms.

Key words: Spherical-cone diaphragms；Residual strain；Multi-expulsion；Arc length method；Finite element method

摘要： 弧长法能跟踪复杂的非线性平衡路径全过程，但计算受初始设定载荷影响较大，而针对这一局限设计的改进算法能更好地求解膜片翻转过程。考虑新型Ti3012合金、纯钛、理想材料，基于改进弧长法研究残余应变对锥柱形膜片多次翻转行为的影响，得出新型Ti3012合金膜片的正翻与回翻过程均没有纯钛膜片好，且存在严重偏心现象，其98%正向翻转状态时回翻过程中不仅偏心量达到60mm，而且出现褶皱等严重失效行为；理想材料在不同正向翻转状态时反向回翻，膜片均存在严重的偏心问题，最大偏心量大于80mm；纯钛膜片仅98%正向翻转状态时回翻过程中偏心量稍大，约为10mm。无残余应变这一材料特性降低了膜片结构刚度，同时伴有初始弹性模量减小的性质，这些因素均不利于膜片多次翻转。

关键词: 锥柱形膜片；残余应变；多次翻转；弧长法；有限元法