平面六节点等参应力奇异单元的精度研究

研究一种平面六节点应力奇异单元的计算精度问题。首先证明该单元具有1/槡r阶奇异性,然后用此单元计算同质材料中的裂纹和双材料界面裂纹的应力强度因子与裂尖应力分布,讨论裂纹尖端奇异单元的尺寸以及在奇异单元与常规单元之间布置一层过渡单元对精度的影响。研究发现,当布置在裂尖的奇异单元边长与裂纹长度的比值在0.1～0.2时,能得到足够精确的解答;而在此范围之外,随奇异单元尺寸进一步增大或减小,精度都会有所下降。对于同质材料中的裂纹以及模量比在10倍之内的双材料界面裂纹,布置过渡单元可以提高精度;而对于模量比大于20倍的界面裂纹,不设置过渡单元的计算结果却与理论解更接近。

STUDY ON THE ACCURACY OF PLANE SIX-NODE ISOPARAMETRIC STRESS SINGULAR ELEMENT

The accuracy of a plane six-node isoparametric stress singular element was stud ied.Firstly,the element was constructed and its 1/r singular ity was proved.Then the element was used in calculations of stress intensity fa ctors and crack tip stress fields for cracks locating both in homogeneous materi al and in interface of bi-materials.The effects of stress singular element siz e and arranging of transition element on the accuracy of the analysis were inves tigated.The results indicated that the proper ratio of element size to the crac k length is in range from 0.1 to 0.2.Beyond this scope,accuracy will declin e with the element size both increase and decrease.For crack in homogeneous mat erial or for interface crack of bi-material,in which the ratio of the two elas tic modules within 10,arrangement of a layer of transition elements between sin gular element and normal element can improve the accuracy.For bi-material inte rface crack with the modulus ratio over 20,however,the results predicted by th e model without transition element are more close to the theoretical ones.