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Effectiveness of the stress solutions in notch/crack tip regions by using extended boundary element method

机译：扩展边界元法在缺口/裂纹尖端区域内应力解的有效性

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摘要

In this paper, the extended boundary element method (XBEM) is employed to evaluate the singular stress fields of plane V-notched/cracked structures based on the linear elastic theory. Firstly, the V-notched/cracked structure is divided into two parts, which are a small region around the notch tip and the outer region without the tip region. Then, the expressions of the asymptotic series expansion of the singular stress fields in the notch tip region are assembled with the boundary integral equation of the outer region without stress singularity. Hence, the displacement and stress fields of both the tip region and outer structure are determined by the XBEM. Three benchmark examples are presented to show that XBEM can obtain the accurate displacement and stress fields from the tip region to the whole region for the V-notched/cracked structures.
机译：本文基于线性弹性理论，采用扩展边界元法（XBEM）来评估平面V形缺口/裂纹结构的奇异应力场。首先，将V形切口/裂纹结构分为两部分，它们是围绕切口尖端的小区域和没有尖端区域的外部区域。然后，利用无应力奇异性的外部区域的边界积分方程，将缺口尖端区域中奇异应力场的渐近级数展开的表达式组合在一起。因此，尖端区域和外部结构的位移场和应力场均由XBEM确定。给出了三个基准示例，以表明XBEM可以获得V形缺口/裂纹结构从尖端区域到整个区域的精确位移和应力场。

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