平面薄膜结构屈曲行为的向量式有限元分析

Analysis of buckling behavior of planar membrane structures based on vector form intrinsic finite element

针对平面薄膜结构在外荷载作用下容易出现局部褶皱和褶皱扩展的现象,分析平面薄膜结构的屈曲行为.基于向量式有限元薄膜单元基本理论,引入面内应力刚化和面外初始缺陷,实现初始预应力平衡状态和触发面外褶皱屈曲变形.推导向量式有限元的力控制和位移控制处理方法,进而跟踪平面薄膜结构的局部褶皱(屈曲)和褶皱扩展(后屈曲)变形全过程.在此基础上,编制平面薄膜结构的屈曲计算分析程序,并通过矩形薄膜剪切屈曲和圆环薄膜扭转屈曲的算例分析,验证理论推导和所编制程序的有效性和正确性.位移控制法可以越过薄膜结构屈曲的极值点(或分支点),有效跟踪屈曲和后屈曲变形的全过程,并获得屈曲临界极限荷载和屈曲下降段.

Aiming at the situation that planar membrane structure is prone to local wrinkling and wrinkling expansion under external loading, buckling behavior of planar membrane structures was studied. Based on the basic theory of membrane element of vector form intrinsic finite element （VFIFE）, in-plane stress stiffening and the out-of-plane initial imperfection were introduced to keep initial prestressed equilibrium state and trigger out-of-plane wrinkling. The force-controlled and displacement-controlled methods of VFIFE were deduced, which were used to track the whole deformation process of local wrinkling （buckling） and wrinkling expansion （post buckling） of planar membrane structures. On this basis, a buckling computer program for planar membrane structures was developed. Analysis of computation examples, such as the shear buckling of rectangular membrane and the torsional buckling of annular membrane, verified the validity and correctness of the theoretical derivation and the computer program. The displacement-controlled method can cross the extremum buckling point （or birfurcation buckling point） of membrane structures and track the whole process of buckling and post buckling effectively. It can also get the critical buckling limit load and the buckling down part.