An over‐deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis
An over‐deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis
复制标题
DOI：
10.1111/j.1460-2695.2010.01504.x
复制
发表时间：
2011-03
影响因子：
3.7
通讯作者：
M. Ayatollahi;M. Nejati
中科院分区：
文献类型：
--
作者：
M. Ayatollahi;M. Nejati
本文采用超确定性方法，用常规有限元法计算裂纹体的应力强度因子和威廉姆斯级数展开式中的高阶项系数。对于裂纹尖端附近的大量节点，得到了一组超定的联立线性方程组，并使用最小二乘法的基本概念，威廉姆斯展开系数可以计算纯模式I，纯模式II和混合模式I/II条件。收敛性的研究已经进行了检查的节点数的影响，在威廉姆斯展开和选定的节点从裂纹尖端的距离，在结果的准确性。结果表明，本文提出的简单方法，即使在粗糙的有限元网格或在没有奇异元素，产生准确的结果。利用文献中已有的结果验证了应力强度因子和高阶项系数的准确性。
An over-deterministic method has been employed for calculating the stress intensity factors (SIFs) as well as the coefficients of the higher-order terms in the Williams series expansions in cracked bodies, using the conventional finite element analysis. For a large number of nodes around the crack tip, an over-determined set of simultaneous linear equations is obtained, and using the fundamental concepts of the least-squares method, the coefficients of the Williams expansion can be calculated for pure mode I, pure mode II and mixed mode I/II conditions. A convergence study has been conducted to examine the effects of the number of nodes used, the number of terms in Williams expansion and the distance of the selected nodes from the crack tip, on the accuracy of the results. It is shown that the simple method presented in this paper, yields accurate results even for coarse finite element meshes or in the absence of singular elements. The accuracy of SIFs and the coefficients of higher-order terms are validated by using the available results in the literature.