屈曲问题有限元模拟的随机缺陷法

Stochastic Defect Method for Finite Element Simulation of Buckling Problems

鉴于目前文献中流行的分支点屈曲问题有限元模拟方法的局限性,提出了对理想构件引入初始随机缺陷,把特征值屈曲问题转化为几何非线性静力变形计算问题进行模拟求解的方法.通过对压杆稳定和弹性地基上梁的屈曲问题的模拟,表明初始随机缺陷法不仅可以计算低阶屈曲模态,而且同样可以得到模型高阶屈曲时的计算结果.在此基础上,指出了有些文献中所使用的影响因子引入缺陷法对非线性问题计算的局限性,并且通过对横向纤维作用下穿透型矩形脱层屈曲问题的计算,分析了初始随机缺陷法对非线性屈曲问题求解的适用性.同时,给出了使用初始随机缺陷法的几种思路和参数选取的建议.

In view of limitations of finite element simulation method of bifurcation buckling in literature,this article presents to introduce stochastic defects in ideal artifacts to transform eigenvalue buckling problems into geometrically nonlinear static deformation problems.The simulation on stability problems of columns and buckling of elastic foundation beam indicates that stochastic defect method can calculate both the first mode and higher modes of buckling.In this article,the first and the second buckling mode by stochastic defect method are presented for stability problems of columns.Furthermore,this article points out limitations of introducing defect by influencing factors in some literature and indicates the applicability of stochastic defect method on nonlinear buckling problems by calculating the buckling of rectangular delamination bridged by fibers.Meanwhile,by contrasting results of different scales defect,this article provides some suggestions to implement this method.