基于整体位移模式的平面裂纹结构数值模拟方法  

A numerical simulation method based on the displacement mode of entirety for plain crack structure

作　　者：郭聪 罗景润[1] GUO Cong;LUO Jing-run(Institute of Systems Engineering,CAEP,Mianyang 621900,China)

机构地区：[1]中国工程物理研究院总体工程研究所,绵阳621900

出　　处：《计算力学学报》2018年第2期249-254,共6页Chinese Journal of Computational Mechanics

摘　　要：对于平面裂纹问题,针对扩展有限元法和无网格伽辽金法的不足,从结构的整体位移模式出发,提出了一种新的数值模拟方法。在整个求解域内构造其试探函数,并引入裂纹修正项描述裂尖处的奇异性和裂纹面的强间断特性;同时,提出了一种新的强制边界条件施加方法,通过引入位移边界水平集函数,将位移边界条件包含在近似位移场的表达式中,有效地解决了位移边界条件问题,减小了刚度矩阵的阶数,非常方便地消除了刚度矩阵的奇异性,降低了线性方程组的求解难度。含裂纹矩形平板结构的数值算例验证了该方法的有效性。A new kind of numerical simulation method for plain crack problem is proposed in the paper which is based on the displacement mode of the entire structure on the consideration of the insufficiency of XFEM and EFGM.In this method,trial functions are constructed within the whole solution area,meanwhile the crack modification terms are introduced in to describe the singularity on the crack tip and the displacement gap on the crack surfaces.This paper also proposes a new kind of method for the displacement boundary problem by introducing displacement level set function and involving the displacement boundary condition in the formula of the approximate displacement field,thus the stiffness matrix size is reduced and the singularity of the matrix is eliminated.As a result the difficulty to solve the linear equation set is decreased.A numerical example of a rectangle plate with crack validates the method.

关 键 词：数值模拟 扩展有限元法 无网格伽辽金法 整体位移模式 刚度矩阵 裂纹 

分 类 号：O346[理学—固体力学]